Home > INT2 > Chapter 12 > Lesson 12.2.3 > Problem12-117

12-117.

For each pair of points given, write an equation for a quadratic function in standard form that has these $x$-intercepts.

1. $(-3, 0)$ and $(2, 0)$

Work backwards: use the zero product property to write an equation in factored form, then simplify.

$x = −3$ or $x = 2$
$x + 3 = 0$ or $x − 2 = 0$
$(x + 3)(x - 2) = 0$
$x^² + x − 6 = y$

1. $(-3, 0)$ and $(\frac { 1 } { 2 }, 0)$

See part (a).

Since we don’t usually factor with fractions, $(x-\frac{1}{2})$
is not considered a factor.

Consider what you would have done to get $\frac{1}{2}$.

If $x = \frac{1}{2}$, the step before that was $2x=2$.