Math

Question Find a quadratic function h(x)h(x) with zeros at x=7x=7 and x=2x=2.

Studdy Solution

STEP 1

Assumptions1. The zeros of the quadratic function are7 and. . A quadratic function with zeros aa and bb can be written in the form h(x)=k(xa)(xb)h(x) = k(x-a)(x-b), where kk is a constant.

STEP 2

We can write the quadratic function h(x)h(x) using the given zeros. Here, a=7a=7 and b=2b=2.
h(x)=k(x7)(x2)h(x) = k(x-7)(x-2)

STEP 3

The constant kk can be any real number. For simplicity, we can choose k=1k=1.
h(x)=1(x7)(x2)h(x) =1(x-7)(x-2)

STEP 4

implify the equation.
h(x)=(x7)(x2)h(x) = (x-7)(x-2)

STEP 5

Expand the equation.
h(x)=x22x7x+14h(x) = x^2 -2x -7x +14

STEP 6

Combine like terms.
h(x)=x29x+14h(x) = x^2 -9x +14So, the quadratic function hh whose zeros are and2 is h(x)=x29x+14h(x) = x^2 -9x +14.

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