Question

write a quadratic function h whose zeros are 13 and 2.
h(x) =

Explanation:

Step1: Recall Zero - Factor Property

If a quadratic function \( h(x) \) has zeros \( r_1 \) and \( r_2 \), then the factored form of the quadratic function is \( h(x)=a(x - r_1)(x - r_2) \), where \( a
eq0 \). For simplicity, we can take \( a = 1 \) (since the problem does not specify a leading coefficient other than the general quadratic form). Here, \( r_1=13 \) and \( r_2 = 2 \).

Step2: Substitute the Zeros into the Factored Form

Substitute \( r_1 = 13 \) and \( r_2=2 \) into the factored form \( h(x)=a(x - r_1)(x - r_2) \). With \( a = 1 \), we get \( h(x)=(x - 13)(x - 2) \).

Step3: Expand the Factored Form

Expand \( (x - 13)(x - 2) \) using the distributive property (FOIL method).
First, multiply the First terms: \( x\times x=x^{2} \).
Then, multiply the Outer terms: \( x\times(- 2)=-2x \).
Next, multiply the Inner terms: \( - 13\times x=-13x \).
Finally, multiply the Last terms: \( - 13\times(-2) = 26 \).
Now, combine like terms: \( x^{2}-2x-13x + 26=x^{2}-15x + 26 \).

Answer:

\( h(x)=x^{2}-15x + 26 \) (or \( h(x)=(x - 13)(x - 2) \) is also a valid quadratic function with the given zeros)