Modeling With Quadratic Functions Worksheet - Section 2.4 Page 2
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8What You Will Learn
What You Will Learn
2.4 Lesson
Write equations of quadratic functions using vertices, points,
and x-intercepts.
Core Vocabulary
Core
Vocabul l
ar
r y
Write quadratic equations to model data sets.
Previous
Writing Quadratic Equations
average rate of change
system of three linear
Core
Core Concept
Concept
equations
Writing Quadratic Equations
Given a point and the vertex (h, k)
Use vertex form:
y = a(x − h)
2
+ k
Given a point and x-intercepts p and q
Use intercept form:
y = a(x − p)(x − q)
Given three points
Write and solve a system of three
equations in three variables.
Writing an Equation Using a Vertex and a Point
The graph shows the parabolic path of a performer who is shot out of a cannon, where
Human Cannonball
y is the height (in feet) and x is the horizontal distance traveled (in feet). Write an
y
equation of the parabola. The performer lands in a net 90 feet from the cannon. What
40
(50, 35)
is the height of the net?
30
SOLUTION
20
From the graph, you can see that the vertex (h, k) is (50, 35) and the parabola passes
(0,15)
10
through the point (0, 15). Use the vertex and the point to solve for a in vertex form.
y = a(x − h)
+ k
2
Vertex form
0
0
20
40
60
80
x
15 = a(0 − 50)
+ 35
2
Horizontal distance
Substitute for h, k, x, and y.
(feet)
−20 = 2500a
Simplify.
−0.008 = a
Divide each side by 2500.
Because a = −0.008, h = 50, and k = 35, the path can be modeled by the equation
y = −0.008(x − 50)
+ 35, where 0 ≤ x ≤ 90. Find the height when x = 90.
2
y =
−0.008(90
− 50)
+ 35
2
Substitute 90 for x.
= −0.008(1600) + 35
Simplify.
= 22.2
Simplify.
So, the height of the net is about 22 feet.
Monitoring Progress
Monitoring Progress
Help in English and Spanish at
1.
WHAT IF?
The vertex of the parabola is (50, 37.5). What is the height of the net?
2.
Write an equation of the parabola that passes through the point (−1, 2) and has
vertex (4, −9).
76
Chapter 2
Quadratic Functions
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