1. Recall Evaluate an Expression
Section 10-2 Exploring Quadratic Graphs SPI 23E: find the solution to a quadratic equation given in standard form SPI 23F: select the solution to a quadratic equation given a graphical representation
Objectives:
Graph quadratic functions
Recall Evaluate an Expression –b 2a
Evaluate the expression for a = –6 and b = 4. –b 2a –4
2(-6) –4
-12 1 3 = = =
Recall Role of 'a' and 'c'
Form of a Quadratic Equation: ax2 + bx + c
Coefficient (a) affects the width of the parabola
Constant (c) affects the movement up or down

2. Role of ‘b’ in a Quadratic Function
Coefficient (b) affects the position of axis of symmetry
vertex moves right or left
axis of symmetry changes
equation of axis of symmetry is x =

3. Explore the Role of ‘b’ when Graphing a Quadratic
Graph the quadratic function y = 2x2 + 4x – 3.
Find the equation of the axis of symmetry.
Substitute values into x =
Find the coordinates of the vertex using the x value.
Substitute x = -1 into the equation to find corresponding y value
y = 2x2 + 4x – 3.
= 2(-1)2 + 4(-1) – 3
= 2 – 4 – 3
= -5
Coordinates of the vertex is (-1, -5)

4. Explore the Role of ‘b’ when Graphing a Quadratic
Graph the quadratic function y = 2x2 + 4x – 3
Vertex is (-1, -5); axis of symmetry is x = -1
3. Find two other points on the graph. x
y = 2x2 + 4x - 3
(x, y) -1
VERTEX from step 2
(-1, -5)
y = 2 (0)2 +4(0) - 3
= -3
(0, -3)
y = 2 (1)2 +4(1) - 3
= 3 1
(1, 3)
3. Reflect points over axis of symmetry
4. Connect with a curved line.

5. Will the curve open down or up? (look at the coefficient of the t2)
Aerial fireworks carry “stars,” which when ignited are projected into the air. 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.
Will the curve open down or up? (look at the coefficient of the t2)
Will the vertex be a max or min point?
Since the coefficient of t 2 is negative, the curve opens downward, and the vertex is the maximum point.
Step 1. Find the x-coordinate of the vertex. b 2a – =
–88
2(–16)
2.75
After 2.75 seconds, the star will be at its greatest height.
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.