Warm Up Solutions

Graph
$y = 4 {(x - \frac{1}{2})}^{2} - 4$

$h = \frac{1}{2}, k = - 4$

Note

To find exact points for the graph, pick values of x to substitute into the equation.

Write the equation in standard form.

$\begin{array}{rcl} 4 (x - \frac{1}{2}) (x - \frac{1}{2}) - 4 & = & 0 \\ 4 (x^{2} - x + \frac{1}{4}) - 4 & = & 0 \\ 4 x^{2} - 4 x + 1 - 4 & = & 0 \\ 4 x^{2} - 4 x - 3 & = & 0 \end{array}$

Solve the equation in problem 2 by factoring.

$4 x^{2} - 4 x - 3 = 0 (2 x + 1) (2 x - 3) = 0 x = - \frac{1}{2}, \frac{3}{2}$

Note

Q: How do the values of x in problem 3 relate to the graph in problem 1?

A: The values of x are the x-intercepts on the graph.