# How do you graph y=-x^2+2x+4?

Jul 14, 2015

Substitute values for $x$, solve for $y$, draw a graph through the points. Be sure to use positive and negative values for $x$.

#### Explanation:

$y = - {x}^{2} + 2 x + 4$

Point A: $\left(- 3 , - 11\right)$

$x = - 3$
$y = - \left({3}^{2}\right) + \left(2 \cdot - 3\right) + 4 = - 9 - 6 + 4 = - 11$

Point B: $\left(- 1 , 1\right)$

$x = - 1$
$y = - \left(- {1}^{2}\right) + \left(2 \cdot - 1\right) + 4 = - 1 - 2 + 4 = 1$

Point C: $\left(0 , 4\right)$

$x = 0$
$y = - \left({0}^{2}\right) + \left(2 \cdot 0\right) + 4 = 4$

Point D: $\left(1 , 5\right)$

$x = 1$
$y = - \left({1}^{2}\right) + \left(2 \cdot 1\right) + 4 = - 1 + 2 + 4 = 5$

Point E: $\left(3 , 1\right)$

$x = 3$
$y = - \left({3}^{2}\right) + \left(2 \cdot 3\right) + 4 = - 9 + 6 + 4 = 1$

Plot the points and draw a graph through the points. It will be a parabola.

graph{y=-x^2+2x+4 [-11.72, 8.28, -3.77, 6.23]}