# `y = x^2 - 6x + 5` Write the quadratic in intercept form and give the function's zeros.

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### Textbook Question

Chapter 5, 5.2 - Problem 16 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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iamkaori | Student, Grade 9 | (Level 2) Salutatorian

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The intercept form is: y = a (x - p) (x - q)

In the given equation y = x^2 - 6x + 5, you can find the x-intercepts.

make y 0, then factor the equation to get:

0 = (x - 5) (x - 1)

so the x intercepts are 5 and 1.

Now, plug in the x- intercepts for p and q.

y = a (x - 1) (x - 5)

Find a by randomly picking a point from the graph and plugging it in. To consume time, you can find the y-intercepts so you have both the 0's for x and y, then plug the y-intercept into the equation.

Find the y-intercept by making x 0 in the original factorised equation.

y = (0 - 5) (0 - 1)

= y = (-5) (-1)

= y = 5

so the y-intercept is 5.

Now, using this point (0,5), plug it into the half-complete intercept form.

5 = a (0 - 1) (0 - 5)

You can tell that this is the same as when trying to solve for the y-intercept, so we can tell that a is 1. So, the final intercept form equation would be:

y = (x - 1) (x - 5)

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