# How do you graph y=-0.5(x+4)(x-6)?

Jul 17, 2018

#### Explanation:

Given: $f \left(x\right) = y = - 0.5 \left(x + 4\right) \left(x - 6\right)$

This function is a quadratic function. When $f \left(x\right) = 0$ you can find the $x$-intercepts (zeros):

$f \left(x\right) = - 0.5 \left(x + 4\right) \left(x - 6\right) = 0$

x + 4 = 0; " "x - 6 = 0

x = -4; " "x = 6

x-intercepts: $\text{ } \left(- 4 , 0\right) , \left(6 , 0\right)$

Put the equation into $y = A {x}^{2} + B x + C = 0$ form. Use FOIL to distribute:

$f \left(x\right) = - 0.5 \left({x}^{2} - 6 x + 4 x - 24\right) = - 0.5 \left({x}^{2} - 2 x - 24\right) = 0$

$f \left(x\right) = - 0.5 {x}^{2} + x + 12 = 0$

The vertex is (-B/(2A), f(-B/(2A))), " axis of symmetry is " x = -B/(2A

$- \frac{B}{2 A} = - \frac{1}{2 \left(- .5\right)} = 1$

$f \left(1\right) = - 0.5 {\left(1\right)}^{2} + 1 + 12 = 12.5$

The vertex is (1, 12.5); " axis of symmetry is " x = 1

You can do point-plotting to find additional points since $x$ is the independent variable:

$\underline{\text{ "x" "|" "y" }}$
$- 3 \text{ "|" } 4.5$
$- 2 \text{ "|" } 8$
$- 1 \text{ "|" } 10.5$
$\text{ "0" "|" } 12$
$\text{ "2" "|" } 12$
$\text{ "3" "|" } 10.5$
$\text{ "4" "|" } 8$

graph{ -0.5(x+4)(x-6) [-10, 10, -5, 15]}