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Warm-Up Exercises
Find the x-intercept and y-intercept.
1. 153x 5y =–
5; 3–ANSWER
+2. 7y 2x=
ANSWER ; 7–2
7
Warm-Up Exercises
ANSWER2
11 ft
3. A ball is thrown so its height h, in feet, is given by
the equation , where t is the time in
seconds. What is the height when t is second?4
1= t 216h 10t+–
Graph a Quadratic Function Using a TableExample 1
Graph y =2
1x 2 1.–
STEP 1 Make a table of values for y Choose
values of x on both sides of the axis of
symmetry x 0.
=2
1x 2 1.–
=
SOLUTION
The function y is in standard form .
Because b 0, you know that the axis of symmetry is
x 0.
=2
1x 2 1–
=
=
x 2ay = + c
Graph a Quadratic Function Using a TableExample 1
y 1
x
7
0
1
2
7
44–
1–
2–
STEP 2 Plot the points from the table.
STEP 3 Draw a smooth curve through the points.
Checkpoint Graph a Quadratic Function Using a Table
Graph the function using a table of values.
ANSWER
1. y = – 3x 2
Checkpoint Graph a Quadratic Function Using a Table
Graph the function using a table of values.
ANSWER
2. y = – x 2 – 2
Checkpoint Graph a Quadratic Function Using a Table
Graph the function using a table of values.
ANSWER
3. y =4
1x 2 3+
Graph a Quadratic Function in Standard FormExample 2
Graph = x 2 6xy 5+–
SOLUTION
The function is in standard form y ax 2 bx c where a 1, b 6, and c 5. Because a > 0, the parabola opens up.
= + += = – =
STEP 1 Draw the axis of symmetry.
STEP 2 Find and plot the vertex. The x-coordinate of the vertex is 3. Find the y-coordinate.
.
= 3x2a
b– = –
2( )1=
6–
Graph a Quadratic Function in Standard FormExample 2
= x 2 6xy 5+–
= 6 5+–( )23 ( )3 = 4–
The vertex is .( )3, 4–
= x 2 6xy 5+– = x 2 6xy 5+–
= 5+–( )20 6( )0 = 5 = 5+–( )21 6( )1 = 0
STEP 3 Plot two points to the left of the axis of symmetry. Evaluate the function for two x-values that are less than 3, such as 0 and 1.
Graph a Quadratic Function in Standard FormExample 2
Plot the points and . Plot their mirror images by counting the distance to the axis of symmetry and then counting the same distancebeyond the axis of symmetry.
( )0, 5 ( )1, 0
STEP 4 Draw a parabola through the points.
Checkpoint Graph a Quadratic Function in Standard Form
Graph the function. Label the vertex and the axis of symmetry.
4. = x 2 6xy 2– –
ANSWER
Checkpoint Graph a Quadratic Function in Standard Form
Graph the function. Label the vertex and the axis of symmetry.
ANSWER
5. = x 2 2xy 1–– +
Checkpoint Graph a Quadratic Function in Standard Form
Graph the function. Label the vertex and the axis of symmetry.
ANSWER
6. = 2x 2 xy 1–+
Example 3 Multiply Binomials
Find the product .( )3+2x ( )7x –
Write products of terms.
SOLUTION
( )7–( )3+2x ( )7x – = 2x( )x + 2x + 3x + 3( )7–
= 2x 2 14x + 3x– 21– Multiply.
= 2x 2 11x– 21– Combine like terms.
Checkpoint Multiply Binomials
Find the product.
7. ( )4x – ( )6x + ANSWER x 2 + 2x 24–
8. ( )1x –( )13x + ANSWER 3x 2 2x 1––
9. –( )52x ( )2x – ANSWER 2x 2 9x 10– +
Example 4 Write a Quadratic Function in Standard Form
Write the function in standard form.
Write original function.
SOLUTION
( )22x –y = 2 5+
( )22x –y = 2 5+
( ) 2x –= 2 5+( ) 2x – Rewrite as .
( )22x –( )2x – ( )2x –
( ) 2xx 2 –= 2 4+2x– 5+ Multiply using FOIL.
( ) 4xx 2 –= 2 4+ 5+ Combine like terms.
8x2x 2 –= 8+ 5+ Use the distributive property.
8x2x 2 –= 13+ Combine like terms.
Checkpoint Write a Quadratic Function in Standard Form
Write the function in standard form.
10. ( )3x –( )1x +y = 2
11. ( )6x –y = 3( )4x –
12. ( )21x –y = 3– –
ANSWER 2x 2 4x 6––y =
ANSWER y = 3x 2 30x 72– +
ANSWER y = x 2 2x 4–+–
