Graphing Quadratic Equations: example 10.50

Graph $y = − x^{2} + 6 x - 9$ .

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.

Graph the parabola $y = −3 x^{2} + 12 x - 12 .$

How did it go?

Graph $y = − x^{2} + 6 x - 9$ .

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.

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

Graph the parabola $y = −3 x^{2} + 12 x - 12 .$

How did it go?

The equation y has on one side.
Since a is $- 1$ , the parabola opens downward. To find the axis of symmetry, find $x = - \frac{b}{2 a}$ .		The axis of symmetry is $x = 3 .$ The vertex is on the line $x = 3 .$
Find y when $x = 3 .$		The vertex is $(3, 0) .$
The y-intercept occurs when $x = 0 .$ Substitute $x = 0 .$ Simplify. The point $(0, −9)$ is three units to the left of the line of symmetry. The point three units to the right of the line of symmetry is $(6, −9) .$ Point symmetric to the y-intercept is $(6, −9)$		The y-intercept is $(0, −9) .$
The x-intercept occurs when $y = 0 .$
Substitute $y = 0 .$
Factor the GCF.
Factor the trinomial.
Solve for x.
Connect the points to graph the parabola.

The equation y has on one side.
Since a is $- 1$ , the parabola opens downward. To find the axis of symmetry, find $x = - \frac{b}{2 a}$ .		The axis of symmetry is $x = 3 .$ The vertex is on the line $x = 3 .$
Find y when $x = 3 .$		The vertex is $(3, 0) .$
The y-intercept occurs when $x = 0 .$ Substitute $x = 0 .$ Simplify. The point $(0, −9)$ is three units to the left of the line of symmetry. The point three units to the right of the line of symmetry is $(6, −9) .$ Point symmetric to the y-intercept is $(6, −9)$		The y-intercept is $(0, −9) .$
The x-intercept occurs when $y = 0 .$
Substitute $y = 0 .$
Factor the GCF.
Factor the trinomial.
Solve for x.
Connect the points to graph the parabola.