Question

Find the vertex and the

�
x​- and
�
y​-intercepts of the equation
�
=
�
2
−
2
�
−
8
y=x
2
−2x−8
Then, use the points to graph the parabola.

a) What is the vertex of the parabola? Enter your answer as an ordered pair.
Vertex
Preview
​
​b) Identify the
�
x​-intercept(s) of the parabola. Enter your answers as ordered pairs. Use a comma to separate answers as needed. If there are none, enter
None
None​.
�
x-intercept
Preview
​
​c) Identify the
�
y​-intercept of the parabola. Enter your answer as an ordered pair.
�
y-intercept
Preview
​
d) Use the points you found to graph the parabola.
​

Answer 1

Explanation:

As seen in earlier sections, the process of completing the square is a useful tool in finding noninteger values of quadratic equations, especially intercepts. When a quadratic equation of the

form f (x) = ax2

+ bx + c is put through the process of completing the square it yields an

equation of the form f (x) = a(x – h)2

+ k . The conversion of the equation to this form will

yield critical information about the equation’s characteristics before you begin to graph it.

1.) The value of h is the distance left (if negative) or right (if positive) the graph

translates from the standard position.

2.) The value of k is the distance up (if positive) or down (if negative) the graph

translates from the standard position.

3.) The values of h and k, when put together as an ordered pair, give the vertex i.e.

(h, k).

4.) The equation x = h is the formula for the axis of symmetry.

The following example demonstrates how to find the following critical information of the

equation:

a.) vertex

b.) axis of symmetry

c.) y intercept (if any)

d.) x intercepts (if any)

Example 1: Find the vertex, axis of symmetry, x-intercept(s), and y-intercept and gr