# `y = x^2 + 10x + 25` Write the quadratic in intercept form and give the function's zeros.

### Textbook Question

Chapter 5, 5.2 - Problem 19 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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Educator Approved

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

All you have to do is put in the problem in a calculator and graph:

y = x^2 + 10x + 25

the graph has a zero at -5, therefore this is the p and the q

intercept form is:

y = a (x - p) (x - q)

plug in the number:

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

y = a (x + 5) (x + 5)

now we have to solve for a. for this we can use any point on the graph. As you can see, the graph crosses the point (-3 , 4) so we can use this coordinate to substitute as x and y

4 = a (-3 + 5) (-3 + 5)

4 = a (2) (2)

4 = 4a

1 = a

so the intercept form is:

y = 1 (x + 5) (x + 5)

Educator Approved

aishukul | Student, Grade 10 | (Level 3) Honors

Posted on

y= (x+5)(x+5) This is the intercept form.

To find the zeros, we can place a zero in exchange for the y.

(x+5)=0

x=-5.

(x+5)=0

x=-5. Both give the zero of -5, so we can assume it is one zero since it's the same number.

Therefore, the zero is -5.