Graphing Quadratic Equations: example 10.52

Graph $y = 2 x^{2} - 4 x - 3$ .

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 $y = 5 x^{2} + 10 x + 3 .$

How did it go?


The equation y has one side. Since a is 2, the parabola opens upward.
To find the axis of symmetry, find $x = - \frac{b}{2 a}$ .		The axis of symmetry is $x = 1$ .
The vertex on the line $x = 1 .$
Find y when $x = 1$ .		The vertex is $(1, − 5)$ .
The y-intercept occurs when $x = 0 .$
Substitute $x = 0 .$
Simplify.		The y-intercept is $(0, −3)$ .
The point $(0, −3)$ is one unit to the left of the line of symmetry. The point one unit to the right of the line of symmetry is $(2, −3)$		Point symmetric to the y-intercept is $(2, −3) .$
The x-intercept occurs when $y = 0$ .
Substitute $y = 0$ .
Use the Quadratic Formula.
Substitute in the values of a, b, c.
Simplify.
Simplify inside the radical.
Simplify the radical.
Factor the GCF.
Remove common factors.
Write as two equations.
Approximate the values.
		The approximate values of the x-intercepts are $(2.5, 0)$ and $(−0.6, 0)$ .
Graph the parabola using the points found.