1. Warm-Up Exercises
Find the product. 1. x + 6 ( ) 3
ANSWER
x 2 18 + 9x 2. x – 5 ( )2
ANSWER
x 2 25 +
10x – x + 5 ( ) 3. – 4
ANSWER
4x 2
100 – 4.
Write y x 8x in standard form. = + ( )
ANSWER
8x 2 5 +
12x

2. Draw the axis of symmetry, x h 2. =
Example 1
Graph a Quadratic Function in Vertex Form
Graph ( )2 2 x – y = 1 +
SOLUTION
The function is in vertex form where , h 2, and k Because a < 0, the parabola opens down. = a 2 – y k + ( )2 h x
STEP 1
Draw the axis of symmetry, x h =
STEP 2
Plot the vertex, ( )
h, k
2, 1 =
STEP 3
Plot points. The x-values 3 and 4 are to the right of the axis of symmetry.

3. One point on the parabola is . ( ) 3, – 1
Example 1
Graph a Quadratic Function in Vertex Form
Plot the points and Then plot their mirror images across the axis of symmetry. ( ) 3, – 1 4, 7 ( )2 2 3 – y = 1 +
One point on the parabola is ( ) 3, – 1 ( )2 2 4 – y = 1 + 7
Another point on the parabola is ( ) 4, – 7 .
STEP 4
Draw a parabola through the points. 3

4. Draw the axis of symmetry. The axis of symmetry is:
Example 2
Graph a Quadratic Function in Intercept Form
Graph y = ( ) 1 x + ( ) 3 x –
SOLUTION
The function is in intercept form where a 1, , and q Because a > 0, the parabola opens up. = p 1 – y ( ) q x a
STEP 1
Draw the axis of symmetry.
The axis of symmetry is: x = q p 2 + 3 1 – 4

5. Find and plot the vertex.
Example 2
Graph a Quadratic Function in Intercept Form
STEP 2
Find and plot the vertex.
The x-coordinate of the vertex is x Calculate the y-coordinate of the vertex. = ( ) 3 x – 1 + y = ( ) 3 1 – + = 4
Plot the vertex ( ) 1, – 4
STEP 3
Plot the points where the x-intercepts occur. The x-intercepts are and q Plot the points and = p 1 – ( )
1, 0
3, 0 5

6. Draw a parabola through the points.
Example 2
Graph a Quadratic Function in Intercept Form
STEP 4
Draw a parabola through the points. 6

7. Graph the function. Label the vertex and the axis of symmetry.
Checkpoint
Graph a Quadratic Function
Graph the function. Label the vertex and the axis of symmetry. 1. ( )2 3 x – y = 1
ANSWER

8. Graph the function. Label the vertex and the axis of symmetry.
Checkpoint
Graph a Quadratic Function
Graph the function. Label the vertex and the axis of symmetry. 2. 3 y = ( )2 2 x – +
ANSWER

9. Graph the function. Label the vertex and the axis of symmetry.
Checkpoint
Graph a Quadratic Function
Graph the function. Label the vertex and the axis of symmetry. 3. 4 y = ( )2 1 x 2 +
ANSWER

10. Graph the function. Label the vertex and the x-intercepts.
Checkpoint
Graph a Quadratic Function
Graph the function. Label the vertex and the x-intercepts. 4. ( ) 7 x – y = 3
ANSWER

11. Graph the function. Label the vertex and the x-intercepts.
Checkpoint
Graph a Quadratic Function
Graph the function. Label the vertex and the x-intercepts. 5. ( ) 5 x – 2 y =
ANSWER

12. Graph the function. Label the vertex and the x-intercepts.
Checkpoint
Graph a Quadratic Function
Graph the function. Label the vertex and the x-intercepts. 6. ( ) 3 x – y = 1 + 2
ANSWER

13. Example 3
Find the Minimum or Maximum Value
Tell whether the function has a minimum value or a maximum value. Then find the minimum or maximum value. ( ) 4 x – 6 + y =
SOLUTION
The function is in intercept form where a , p , and q Because a < 0, it has a maximum value. Find the y-coordinate of the vertex. ( ) q x – y = a p x = q p 2 + 4 6 – 1 ( ) 4 x – 6 + y = 1
100

14. The maximum value of the function is 100.
Example 3
Find the Minimum or Maximum Value
ANSWER
The maximum value of the function is 100. 14

15. Find the height of the cable above the road, when the
Example 4
Using a Quadratic Function
Civil Engineering The Golden Gate Bridge in San Francisco, CA, has two towers. The top of each tower is 500 feet above the road. The towers are connected by suspension cables. Each cable forms a parabola with the equation where x and y are measured in feet. y = 8 1
8690 – ( )2
2100 x +
Find the height of the cable
above the road, when the
cable is at the lowest point.
The road is represented by y a. = 15

16. What is the distance d between the towers? b.
Example 4
Using a Quadratic Function
What is the distance d between the towers? b.
SOLUTION
The function is in vertex form where . a = 1
8690
2100, , h
and k 8
The vertex is The height of the cable at its lowest point is the y-coordinate of the vertex. So, the cable is 8 feet above the road. a. ( )
h, k
2100, 8 = 16

17. distance between the towers is 2100 2100 4200 feet.
Example 4
Using a Quadratic Function b.
The vertex is 2100 feet from the left tower. The axis of symmetry passes through the vertex. So, the vertex is also 2100 feet from the right tower. The
distance between the towers is feet. + = 17

18. Checkpoint
Find the Minimum or Maximum Value
Tell whether the function has a minimum or maximum value. Then find the minimum or maximum value. 7. ( )2 8 x y = 12 – 2 1 +
ANSWER
minimum; 12 –
ANSWER
minimum; – 4 27 8. ( ) 7 x – y = 3 4 ( ) 4 x + y = 9.
ANSWER
minimum; 4 –