1. Graph the function y = 2x2 + 4x – 3.
Quadratic Functions
ALGEBRA 1 LESSON 8-3
Graph the function y = 2x2 + 4x – 3.
Step 1: Find the equation of the axis of symmetry and the
coordinates of the vertex.
Find the equation of the axis of symmetry.
x = b 2a – = –4
2(2)
= – 1
The x-coordinate of the vertex is –1.
y = 2x2 + 4x – 3
y = 2(–1)2 + 4(–1) – 3
= –5
To find the y-coordinate of the vertex, substitute –1 for x.
The vertex is (–1, –5).
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2. Step 2: Find two other points. Use the y-intercept.
Quadratic Functions
ALGEBRA 1 LESSON 8-3
(continued)
Step 2: Find two other points.
Use the y-intercept.
For x = 0, y = –3, so one point is (0, –3).
Choose a value for x on the same side of the vertex.
Let x = 1
y = 2(1)2 + 4(1) – 3  
= 3
For x = 1, y = 3, so another point is (1, 3).
Find the y-coordinate for x = 1.
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3. Quadratic Functions (continued)
ALGEBRA 1 LESSON 8-3
(continued)
Step 3: Reflect (0, –3) and (1, 3) across the axis of symmetry to get two more points.
Then draw the parabola.
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4. Quadratic Functions
ALGEBRA 1 LESSON 8-3
Aerial fireworks carry “stars,” which are made of a sparkler-like material, upward, ignite them, and project them into the air in fireworks displays. Suppose a particular star is projected from an aerial firework at a starting height of 610 ft with an initial upward velocity of 88 ft/s. How long will it take for the star to reach its maximum height? How far above the ground will it be?
The equation h = –16t2 + 88t gives the height of the star h in feet at time t in seconds.
Since the coefficient of t 2 is negative, the curve opens downward, and the vertex is the maximum point.
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5. Step 1: Find the x-coordinate of the vertex.
Quadratic Functions
ALGEBRA 1 LESSON 8-3
(continued)
Step 1:  Find the x-coordinate of the vertex.
After 2.75 seconds, the star will be at its greatest height. b 2a – =
–88
2(–16)
2.75
Step 2:  Find the h-coordinate of the vertex.
h = –16(2.75)2 + 88(2.75) Substitute 2.75 for t.
h = Simplify using a calculator.
The maximum height of the star will be about 731 ft.
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6. Graph the quadratic inequality y > –x2 + 6x – 5.
Quadratic Functions
ALGEBRA 1 LESSON 8-3
Graph the quadratic inequality y > –x2 + 6x – 5.
Graph the boundary curve, y = –x2 + 6x – 5.
Use a dashed line because the solution of the inequality y > –x2 + 6x – 5 does not include the boundary.
Shade above the curve.
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7. Graph each relation. Label the axis of symmetry and the vertex.
Quadratic Functions
ALGEBRA 1 LESSON 8-3
Graph each relation. Label the axis of symmetry and the vertex.
1. y = x2 – 8x + 15
2. ƒ(x) = –x2 + 4x – 2 1 4
<
3. y – x2 – 2x – 6
x = –4
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