8.11.4 • Writing Quadratics When Given Any Format

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In this lesson, you have learned how to write a quadratic function from different starting contexts and when provided different information.

1.

Identify a quadratic function in standard form, $b (x)$ , with the zeros –6 and 8.

Compare your answer:

$b (x) = x^{2} - 2 x - 48$

2.

Identify a quadratic function in standard form, $m (x)$ , with the given zero.

Compare your answer:

$m (x) = x^{2} - 12 x + 36$

3.

Write the specific quadratic function, $d (x)$ , in standard form, that has the zeros 2 and 5 and passes through the point $(1, 16)$ .

Compare your answer:

Intercept form: $d (x) = a (x - 2) (x - 5)$

Find the value of $a$ . Use point $(1, 16)$ .

$d (x) = a (x - 2) (x - 5)$

$16 = a ((1) - 2) ((1) - 5)$

$16 = a (- 1) (- 4)$

$16 = 4 a$

$4 = a$

Substitute 4 for $a$ .

$d (x) = a (x - 2) (x - 5)$

$d (x) = 4 (x - 2) (x - 5)$

$d (x) = 4 (x^{2} - 2 x - 5 x + 10)$

$d (x) = 4 (x^{2} - 7 x + 10)$

$d (x) = 4 x^{2} - 28 x + 40$

So, the specific quadratic function written in standard form is $d (x) = 4 x^{2} - 28 x + 40$ .

8.11.4 Writing Quadratics When Given Any Format