Question

WORTH 100 POINTS!

Answer 1

Answer:

Step-by-step explanation:

4. h(x) = 2x^2 + 14x - 60

Step-by-step explanation:

Given that h(x) is a quadratic.

Also, h(3) = h(-10) = 0

(A) h(x) = x^2 - 13x - 30

=> h(3) = 3^2 - 13(3) - 30

=> h(3) = 9 - 39 - 30

=> h(3) = -30 - 30

=> h(3) = -60

=> h(3) ≠ 0

(B) h(x) = x^2 - 7x - 30

=> h(3) = 3^2 - 7(3) - 30

=> h(3) = 9 - 21 - 30

=> h(3) = -12 - 30

=> h(3) = -42

=> h(3) ≠ 0

(C) h(x) = 2x^2 + 26x - 60

=> h(3) = 2(3^2) + 26(3) - 60

=> h(3) = 2(9) + 78 - 60

=> h(3) = 18 + 78 - 60

=> h(3) = 96 - 60

=> h(3) = 36

=> h(3) ≠ 0

(D) h(x) = 2x^2 + 14x - 60

=> h(3) = 2(3^2) + 14(3) - 60

=> h(3) = 2(9) + 42 - 60

=> h(3) = 18 + 42 - 60

=> h(3) = 60 - 60

=> h(3) = 0

And

=> h(-10) = 2(-10)^2 + 14(-10) - 60

=> h(-10) = 2(100) - 140 - 60

=> h(-10) = 200 - 200

=> h(-10) = 0

Clearly we have,

=> h(3) = h(-10) = 0

Hence, the correct option is (D) h(x) = 2x^2 + 14x - 60

Answer 2

Answer:

h(x) = 2x^2 +14x -60

Step-by-step explanation:

A quadratic is of the form

h(x) = ax^2 + bx +c

h(3) = h(-10) = 0

This tells us that the zeros are at x=3 and x = -10

We can write the equation in the form

h(x) = a( x-z1)(x-z2) where z1 and z2 are the zeros

h(x) = a(x-3) (x- -10)

h(x) = a(x-3) (x+10)

FOIL

h(x) = a( x^2 -3x+10x-30)

h(x) = a(x^2 +7x -30)

Let a = 2

h(x) = 2x^2 +14x -60