Find the Axis of Symmetry y+7=3(x-1)^2

$y + 7 = 3 {(x - 1)}^{2}$

Step 1

Subtract $7$ from both sides of the equation.

$y = 3 {(x - 1)}^{2} - 7$

Step 2

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = 3$

$h = 1$

$k = - 7$

Step 3

Since the value of $a$ is positive, the parabola opens up.

Opens Up

Step 4

Find the vertex $(h, k)$ .

$(1, - 7)$

Step 5

Find $p$ , the distance from the vertex to the focus.

Find the distance from the vertex to a focus of the parabola by using the following formula.

$\frac{1}{4 a}$

Substitute the value of $a$ into the formula.

$\frac{1}{4 \cdot 3}$

Multiply $4$ by $3$ .

$\frac{1}{12}$

Step 6

Find the focus.

The focus of a parabola can be found by adding $p$ to the y-coordinate $k$ if the parabola opens up or down.

$(h, k + p)$

Substitute the known values of $h$ , $p$ , and $k$ into the formula and simplify.

$(1, - \frac{83}{12})$

Step 7

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

$x = 1$

Step 8