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Question 5

Which of the following functions best describes this graph?
4
Ay=x²-2x+4
OB. y +9x+18
OC. ys (x+5)(x-4)

Question 5 Which of the following functions best describes this graph? 4 Ay=x²-2x-example-1
User Hearner
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1 Answer

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Answer:

D. y = (x - 3)(x - 6)

Explanation:

The graph shows a parabola and the parabola intersects the x-axis at (-6, 0) and at (-3, 0). When a function intersects the x-axis, the y value must automatically equal 0, since there is only horizontal movement on the x-axis.

(x-3)(x-6) is a binomial expression that will make a quadratic equation when expanded. We refer to the coordinate where a parabola intersects the x-axis as roots, which are numbers that make the quadratic equation equal 0.

We know from the zero-product property, that when the product of two numbers is 0, at least on the numbers must be 0 (e.g., 4 * 0 = 0 or even 0 * 0 = 0). Thus, we can solve any quadratic equation in the the x-intercept form (i.e., the form tha (x-3)(x-6) is currently in) by setting both expressions equal to 0 and solving for x. This wil give an x-coordinate both times, but since you set the equations equal to 0, you know that your y-coordinate each time is 0:

Solution for x - 3 = 0:

x - 3 = 0

x = 3

Solving for x - 6 = 0

x - 6 = 0

x = 6

You can check by plugging in 3 for x and 6 for x and see if you get 0:

3 for x:

(3 - 3)(3 - 6) = 0

0 * -3 = 0

0 = 0

6 for x:

(6 - 3)(6 - 6) = 0

3 * 0 = 0

0 = 0

User Aresz
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