1Cademy - Graphing $$x = -4(y+2)^2 + 4$$

Learn Before

Graphing a Horizontal Parabola Using Properties

Example

Graphing $x = -4(y+2)^2 + 4$

To graph the horizontal parabola $x = -4(y+2)^2 + 4$ using its properties, first identify the constants $a$ , $h$ , and $k$ . Here, $a = -4$ , $h = 4$ , and $k = -2$ . Since $a$ is negative, the parabola opens to the left. The axis of symmetry is the horizontal line $y = -2$ . The vertex is $(4, -2)$ . To find the $x$ -intercept, substitute $y = 0$ : $x = -4(0+2)^2 + 4 = -4(4) + 4 = -12$ . The $x$ -intercept is $(-12, 0)$ . The point symmetric to $(-12, 0)$ across the axis of symmetry is $(-12, -4)$ . To find the $y$ -intercepts, set $x = 0$ : $0 = -4(y+2)^2 + 4$ , which gives $1 = (y+2)^2$ . Solving yields $y+2 = \pm 1$ , so $y = -1$ and $y = -3$ . The $y$ -intercepts are $(0, -1)$ and $(0, -3)$ . Plot these points to complete the graph.

0

1

Updated 2026-06-05

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related

Learn After