*x*- and

*y*-intercepts and solve any quadratic equation. Now we will learn an easy method used to graph them.

The graph of a quadratic equation is called a parabola.

*x*-values and finding their corresponding

*y*-values.

**Graph**:

The more points we plot the easier it is to see that the graph is u-shaped. The

**, in this case, is the point where the graph changes from decreasing to increasing, or the point with the smallest***vertex**y*-value. Here the vertex is (0, 0) which is also the*x*- and*y*-intercept. The line*x*= 0, the*y*-axis, is the**. This is the line where we could fold our paper to see that the two sides of the graph coincide.***line of symmetry***Given the graph find the**

*x*- and*y*-intercepts, vertex, a 5th point on the graph and the line of symmetry.
Line of symmetry:

*x*= 1
x-intercepts: (-2,0) and (4,0)

y-intercept: (0, -8)

Vertex: (1, -9)

5th point: (2, -8)

Recall that two points determine a line - this is not the case for parabolas. Parabolas require a minimum of 3 points but we usually want to find at least five points to make a nice graph. Find the vertex,

*x*- and

*y*- intercepts as well as the line of symmetry.

**Graph:**

**Step 1**: Find the

*y*-intercept, (0,

*c*).

**Step 2**: Find the

*x*-intercepts by setting

*y*= 0 and solving for

*x*.

**Step 3**: Find the vertex. You can find the x-value of the vertex using the vertex x = -b/(2a).

**Step 4**: Graph the points and identify the axis of symmetry.

*y*-value of −1, this will be an important fact when working the word problems.

**Tip**: The axis of symmetry of any quadratic function will be the vertical line

*x*-intercepts where the resulting quadratic equation does not factor, simply use the quadratic formula to solve it.

**Graph:**

*y*-intercept.

**Graph and label all important points**:

**Graph and label all important points**:

*y*-value is −5. It turns out that not all parabolas have two

*x*-intercepts as we would expect. Sometimes they have only one

*x*-intercept and sometimes none.

*y*-intercept. In addition, we will still be able to find another point using symmetry. So in some cases it is acceptable to plot and label only three points.

**Graph and label all important points:**

**Graph and label all important points:**

**Projectile Problem**: An object is thrown from a 100 foot building at an initial speed of 44 feet per second. How long will it take to reach the maximum height? What is the maximum height?

**Video Examples on YouTube**: