Question

HELP ME!!!!!! h(x) = -(x + 2)2 + 8 what is the axis of Symmetry

Answer 1

Answer:

The vertical line $x = -2$ is the axis of symmetry of $y = -(x + 2)^{2} + 8$.

Step-by-step explanation:

For the graph of a quadratic function, the axis of symmetry is the vertical line that goes through the vertex of this function.

In general, if the vertex of a quadratic function is at $(x_{0},\, y_{0})$, the vertex form equation of this function would be $y = a\, (x - x_{0})^{2} + y_{0}$ for some non-zero constant $a$ ($a \ne 0$.)

Rewrite the quadratic equation in this question $y = -(x + 2)^{2} + 8$ to match the vertex form:

$y = -(x + 2)^{2} + 8$.

$y = (-1)\, (x - (-2))^{2} + 8$.

Thus:

• $a = (-1)$.
• $x_{0} = (-2)$.
• $y_{0} = 8$.

Hence, the vertex of this parabola would be at $(-2,\, 8)$.

Again, the axis of symmetry of this graph would be a vertical line that goes through this vertex. The $x$-coordinate of this vertical line would be $(-2)$. The equation of this vertical line would be $x = (-2)$.

Hence, the axis of symmetry of this quadratic function would be $x = (-2)$.