# How do you graph #y=x^2-9#?

##### 2 Answers

Please read the explanation.

#### Explanation:

A **quadratic equation** is of the form:

We have :

Set

We have the **quadratic equation:**

Using the **algebraic identity**:

We can rewrite

Hence, there are **two solutions** for

So, we have **two x-intercepts:**

To find the **y-intercept**, set

Hence, the **y-intercept**:

The graph of

Hope it helps.

Refer to the explanation.

#### Explanation:

Given:

where:

To graph a quadratic equation in standard form, you need the vertex, y-intercept, x-intercepts (if real), and one or two additional points.

**Vertex: maximum or minimum point #(x,y)# of the parabola**

Since

The x-coordinate of the vertex is determined using the formula for the axis of symmetry:

To find the y-coordinate of the vertex, substitute

**The vertex is #(0,-9)# Plot this point.**

In this case, the vertex is also the y-intercept, which is the value of

**X-intercepts: values for #x# when #y=0#**

Substitute

Switch sides.

Factor

Set each binomial equal to

**Point: #(-3,0)# Plot this point.**

**Point: #(3,0)# Plot this point.**

**For additional points, choose values for #x# and solve for #y#.**

Plot all the points and sketch a parabola through the points. Do not connect the dots.

graph{y=x^2-9 [-11.13, 11.37, -9.885, 1.365]}