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Use the quadratic formula to solve the equation, 0 is equal to negative 7q squared plus 2q plus 9. Now, the quadratic formula, it applies to any quadratic equation of the form-- we could put the 0 on the left hand side. 0 is equal to ax squared plus bx plus c. And we generally deal with x's, in this problem we're dealing with q's. But the quadratic formula says, look, if you have a quadratic equation of this form, that the solutions of this equation are going to be x is going to be equal to negative b plus or minus the square root of b squared minus 4ac-- all of that over 2a. And this is actually two solutions here, because there's one solution where you take the positive square root and there's another solution where you take the negative root. So it gives you both roots of this. So if we look at the quadratic equation that we need to solve here, we can just pattern match. We're dealing with q's, not x's, but this is the same general idea. It could be x's if you like. And if we look at it, negative 7 corresponds to a. That is our a. It's the coefficient on the second degree term. 2 corresponds to b. It is the coefficient on the first degree term. And then 9 corresponds to c. It's the constant. So, let's just apply the quadratic formula. The quadratic formula will tell us that the solutions-- the q's that satisfy this equation-- q will be equal to negative b. b is 2. Plus or minus the square root of b squared, of 2 squared, minus 4 times a times negative 7 times c, which is 9. And all of that over 2a. All of that over 2 times a, which is once again negative 7. And then we just have to evaluate this. So this is going to be equal to negative 2 plus or minus the square root of-- let's see, 2 squared is 4-- and then if we just take this part right here, if we just take the negative 4 times negative 7 times 9, this negative and that negative is going to cancel out. So it's just going to become a positive number. And 4 times 7 times 9. 4 times 9 is 36. 36 times 7. Let's do it up here. 36 times 7. 7 times 6 is 42. 7 times 3, or 3 times 7 is 21. Plus 4 is 25. 252. So this becomes 4 plus 252. Remember, you have a negative 7 and you have a minus out front. Those cancel out, that's why we have a positive 252 for that part right there. And then our denominator, 2 times negative 7 is negative 14. Now what does this equal? Well, we have this is equal to negative 2 plus or minus the square root of-- what's 4 plus 252? It's just 256. All of that over negative 14. And what's 256? What's the square root of 256? It's 16. You can try it out for yourself. This is 16 times 16. So the square root of 256 is 16. So we can rewrite this whole thing as being equal to negative 2 plus 16 over negative 14. Or negative 2 minus-- right? This is plus 16 over negative 14. Or minus 16 over negative 14. If you think of it as plus or minus, that plus is that plus right there. And if you have that minus, that minus is that minus right there. Now we just have to evaluate these two numbers. Negative 2 plus 16 is 14 divided by negative 14 is negative 1. So q could be equal to negative 1. Or negative 2 minus 16 is negative 18 divided by negative 14 is equal to 18 over 14. The negatives cancel out, which is equal to 9 over 7. So q could be equal to negative 1, or it could be equal to 9 over 7. And you could try these out, substitute these q's back into this original equation, and verify for yourself that they satisfy it. We could even do it with the first one. So if you take q is equal to negative 1. Negative 7 times negative 1 squared-- negative 1 squared is just 1-- so this would be negative 7 times 1, right? That's negative 1 squared. Negative 1 times 2 is minus 2 plus 9. So it's negative 7 minus 2, which is negative 9, plus 9, does indeed equal 0. So this checks out. And I'll leave it up to you to verify that 9 over 7 also works out.

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Using the quadratic formula | Algebra (video) | Khan Academy

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Use the quadratic formula to solve the equation, 0 is equal to negative 7q squared plus 2q plus 9. Now, the quadratic formula, it applies to any quadratic equation of the form-- we could put the 0 on the left hand side. 0 is equal to ax squared plus bx plus c.

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A type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed , periodic inter val.

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A measure of how far a data point is above or below the population mean expressed i standard deviation. The difference between a data point and population mean , divided by the population standard deviation.

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The empirical rule shows that 68% will fall within the first standard deviation , 98% will fall within the first two standard deviation and 99.7% will fall within the first three standard deviations of the mean .

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The difference between the lowest and highest values. Range can also mean all the output values of a function.

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The mode of a set of numbers is the one that occurs most often .

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To find the median place the numbers you are given in value and find the middle number

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The mean is the average of the numbers a calculated" central" value of a set of numbers. To calculate just add up all the numbers the divide by how many there are.

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Is a measure of how spread out numbers are , it is the squared root of the Variance, and the variance is the average of the squared difference from the mean .

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a number that produces a specified quantity when multiplied by itself

7 is a square root of 49

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unit measurement of an angle.

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the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159

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The area of a flat, or plane figure is the number of unit squares that can be contained within it.

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a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent,

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has two angles congruent to each other in it, which means the sides opposite those angles - the two legs - will also be congruent. The two legs are the same length. If you know the hypotenuse, then both legs have a length equal to the hypotenuse's length divided by sqrt(2).

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special triangles in trigonometry. One is the 30°-60°-90° triangle. The other is the isosceles righttriangle. They are special because, with simple geometry, we can know the ratios of their sides. Theorem.

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is the height from the mean, or rest, value of the function to its maximum or minimum.

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Sine, in mathematics, is a trigonometric function of an angle. The sine of an angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite thatangle to the length of the longest side of the triangle

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https://www.youtube.com/watch?v=MklXVaTtlhs

Using this triangle (lengths are only to one decimal place):

sin(35°) | = Opposite / Hypotenuse
= 2.8 / 4.9
= 0.57...
cos(35°) | = Adjacent / Hypotenuse
= 4.0 / 4.9
= 0.82...
tan(35°) | = Opposite / Adjacent
= 2.8 / 4.0
= 0.70...

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A way of remembering how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent.

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draw (a figure) within another so that their boundaries touch but do not intersect.

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circle sector (symbol: ⌔), is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the majorsector

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2πR is the circumference of the whole circle. Remember that the circle is 360 degrees.

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= π × diameter = 2 × π × radius. It is the perimeter of a circle

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The length of a line from the center to the circumference

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The Opposite of an operation or number.

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A= P(1+ r/n)^nt

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Multiply exponent with the same base. 2^6

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straight lines of the equation , toward which a function f(x) approaches infinitesimally closely, but never reaches the line, as f(x) increases without bound.

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For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontallines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotesare vertical lines near which the function grows without bound.

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to eliminate by striking out a factor common to both the denominator and numerator of a fraction, equivalent terms on opposite sides of an equation

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the least commonmultiple of the denominators of a set of fractions.

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A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point.

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The end behavior of a polynomial function is thebehavior of the graph of f(x) as x approaches positive infinity or negative infinity.

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arithmetical division in which the divisor has two or more figures, and a series of steps

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a shorthand, or shortcut, method of polynomialdivision in the special case of dividing by a linear factor

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The lowest point in a parabola that opens down

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The highest point of a parabola that opens down

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To take away from.

8-4

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Adding to or going up

4+5+

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A Number, multiplied by itself numerous times. Example: 9 squared= 81.

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The X coordinates of the points where the graph meets the X-Axis.

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A number x multiplied by itself multiple times to get a certain number. Example 3x3=

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1. a fixed line used in describing a curve or surface.

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a number or quantity that when multiplied by itself, typically a specified number of times, gives a specified number or quantity.

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Quanity of a number 0

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the least or smallest amount or quantity possible, attainable, or required.

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as great, high, or intense as possible or permitted.

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the set of values that a given function can take as its argument varies.

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the set of possible values of the independent variable or variables of a function.

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a number or quantity that when multiplied with another produces a given number or expression.

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a number that is multiplyed by itself gives a number

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the distance to the focus equals the distance to the directix

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The multiply out the parts of an of an expression

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a relation from a set of inputs to a set of possible outputs where each input is related to exatly one point

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Any and all value(s) of the variable(s) that satisfies an equation.

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any real numbers that cannot be expressed as a ratio integers cannot repeat decimals

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any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator, q, not equal to zero.

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A number with no fractions or integers

any whole number would be 1,2,3,4,5,6,7,8,9,10 and above

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the total amount resulting from the addition of two or more numbers, amounts, or items

1+3=4 (4 is the sum)

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To make the equation as simple as possible

2/4= 1/2

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to figure out the answer

4+10=14

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a mathematical relationship or rule expressed in symbols

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is an equality containing one or more variables

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A branch of mathmatics dealing with the collection , analysis , interpretation and presentation of masses of numerical data

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a circle with a radius of one.

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Branch of mathematics that studies relationships involving lengths and angles of triangles

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Is a triangle in which one angle is a right angle(that is, a 910 degree angle).

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Is a triangle in which one angle is a right angle( that is, a 90 degree angle).

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A 3 sides shade that is 180 degrees

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Y=a6x is X=6^y

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A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials.

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An expression with two or more terms.

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an equation where the highest exponent of the variable usually X is a square (2)

ax²+bx+c = 0