Question

Write a quadratic function in standard form having zeros of -9 and -12

Answer 1

(x + 9)(x + 12) = 0
Expanding the brackets, we get:
$x^{2}+21x+108=0$

Answer 2

A quadratic equation can be written in standard form or as a parabola

The quadratic equation in standard form is $y = x^2 + 21x + 108$

The zeros of the quadratic function are given as:

$x = -9$

$x = -12$

Equate both zeros to 0

$x + 9 = 0$

$x+12 = 0$

Multiply both zeros

$(x + 9) \times (x + 12) = 0 \times 0$

Expand

$x(x + 12)+ 9(x + 12) = 0 \times 0$

Expand the above expression

$x^2 + 12x+ 9x + 108 = 0$

Add like terms

$x^2 + 21x + 108 = 0$

Replace 0 with y

$x^2 + 21x + 108 = y$

Rewrite the equation as

$y = x^2 + 21x + 108$

Hence, the quadratic equation in standard form is $y = x^2 + 21x + 108$

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