Graphing Quadratic Equations: example 10.45

For the parabola $y = 3 x^{2} - 6 x + 2$ find: ⓐ the axis of symmetry and ⓑ the vertex.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

For the parabola $y = 2 x^{2} - 8 x + 1$ find: ⓐ the axis of symmetry and ⓑ the vertex.

How did it go?

ⓐ
The axis of symmetry is the line $x = - \frac{b}{2 a}$ .
Substitute the values of a, b into the equation.
Simplify.		$x = 1$
		The axis of symmetry is the line $x = 1$ .
ⓑ
The vertex is on the line of symmetry, so its x-coordinate will be $x = 1$ .
Substitute $x = 1$ into the equation and solve for y.
Simplify.
This is the y-coordinate.		$y = −1$ The vertex is $(1, − 1) .$

ⓐ
The axis of symmetry is the line $x = - \frac{b}{2 a}$ .
Substitute the values of a, b into the equation.
Simplify.		$x = 1$
		The axis of symmetry is the line $x = 1$ .
ⓑ
The vertex is on the line of symmetry, so its x-coordinate will be $x = 1$ .
Substitute $x = 1$ into the equation and solve for y.
Simplify.
This is the y-coordinate.		$y = −1$ The vertex is $(1, − 1) .$