### Home > INT3 > Chapter 8 > Lesson 8.1.2 > Problem8-33

8-33.

For each set of points given below, write a possible equation for a quadratic function in standard form. Homework Help ✎

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

These are the $x$-intercepts, so work backwards by using the Zero Product Property to write an equation in factored form.

$\left(x - \frac{1}{2}\right)\, \, \rightarrow \, \, (2x-1)$

$y = 2x^{2} + 5x – 3$

1. $( - 3,0 ) , ( 2,0 ) , \text { and } ( 3 , - 12 )$

See part (a).

$y=a(x+3)(x-2)$

Now substitute in the coordinates of the point $\left(3, −12\right)$ to solve for $a$.