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Using The Quadratic Formula to Sketch Graphs
Principles of Economics 2 (BEA121)
University of Tasmania
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Math 154B Name_____________________ Solving Using the Quadratic Formula Worksheet
The Quadratic Formula: For quadratic equations: ax 2 bx c 0 ,
a
b b ac x 2
24
Solve each equation using the Quadratic Formula. 1. 4 x 211 x 20 0 2. x 25 x 24 0
x 23 x 3
- x 255 x
x 2 x 1
- 4 x 218 x
4 x 27 x 15 0
8. x 23 x 10 0
9. x 2 x 3
10. 2 x 22314 x
11. x 22 x 48
12. 2 x 23918 x
13. 5 x 23 x 1 0 14. 5 x 250 x 125
Answers:
- , 4 4
x 5 x
x ,8 x 3
2
x 321
4.
2
x 55
5.
2
x 15
6.
2
x 25
7. , 3
4
x 5 x
x ,2 x 5
2
x 113
10.
2
x 73
11. x ,8 x 6
12.
2
9 3
x
- x = not a real number
- x 5
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Kuta Software - Infinite Algebra 2 Name___________________________________
Properties of Parabolas Date________________ Period____
Identify the vertex of each.
- y = x 2 + 16 x + 64 2) y = 2 x 2 − 4 x − 2
3)
y = − x 2 + 18 x − 75 4) y = − x 2 + 12 x − 10
Graph each equation.
- y = x 2 − 2 x − 3
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
6)
y = − x 2 − 6 x − 10
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
Identify the min/max value of each. Then sketch the graph.
- f ( x ) = − x 2 + 8 x − 20
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
- f ( x ) = −
1
3
x 2 +
4
3
x −
16
3
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
-1-
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- f ( x ) = x 2 + 2 x − 1
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
- f ( x ) = − x 2 − 10 x − 30
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
Identify the vertex, axis of symmetry, and min/max value of each.
f ( x ) = 3 x 2 − 54 x + 241 12) f ( x ) = x 2 − 18 x + 86
f ( x ) = −
4
5
x 2 +
48
5
x −
114
5
f ( x ) = − x 2 − 20 x − 46
f ( x ) = −
1
4
x 2 + 7
f ( x ) = x 2 − 12 x + 44
f ( x ) =
1
4
x 2 − x + 9
- f ( x ) = x 2 + 4 x + 5
-2-
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- f ( x ) = x 2 + 2 x − 1
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8 Min value = −
- f ( x ) = − x 2 − 10 x − 30
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8 Max value = −
Identify the vertex, axis of symmetry, and min/max value of each.
- f ( x ) = 3 x 2 − 54 x + 241
Vertex: ( 9 , −2)
Axis of Sym.: x = 9 Min value = −
- f ( x ) = x 2 − 18 x + 86
Vertex: ( 9 , 5 )
Axis of Sym.: x = 9 Min value = 5
- f ( x ) = −
4
5
x 2 +
48
5
x −
114
5
Vertex: ( 6 , 6 )
Axis of Sym.: x = 6 Max value = 6
- f ( x ) = − x 2 − 20 x − 46
Vertex: (−5, 4 )
Axis of Sym.: x = − Max value = 4
- f ( x ) = −
1
4
x 2 + 7
Vertex: ( 0 , 7 )
Axis of Sym.: x = 0 Max value = 7
- f ( x ) = x 2 − 12 x + 44
Vertex: ( 6 , 8 )
Axis of Sym.: x = 6 Min value = 8
- f ( x ) =
1
4
x 2 − x + 9
Vertex: ( 2 , 8 )
Axis of Sym.: x = 2 Min value = 8
- f ( x ) = x 2 + 4 x + 5
Vertex: (−2, 1 )
Axis of Sym.: x = − Min value = 1
-2-
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware
Sketching Quadratic Equations
A sketch graph of a quadratic function should illustrate the following:
The general shape of the graph (i. whether there is a maximum or a minimum) with respect to the x- and y- axes.
The location of the y-intercept (mark on the coordinates)
The roots of the equation (label the location on the x-axis)
The location of the vertex (mark on the coordinates)
You DO NOT need to measure out an accurate scale on a sketch graph, as long as you have provided the information listed above.
Sketch graphs of the following quadratic equations, showing y-intercepts, roots, and the vertex.
a. y x 2 11 x 10 b. y x 2 12 x 32
c. y x 2 6 x 5 d. y x 2 8 x 15
e. y x 2 12 x f. y x 2 5 x
g. y x 2 10 x 21 h. y x 2 11 x 10
i. y 2 x 2 13 x 7 j. y 2 x 2 5 x 12
k. l. y x 2 4 x 4 y x 2 6 x 9
g. shape: x 2 y–intercept: (0, – 21) Roots: (3, 0) and (7, 0) Vertex: (5, 4)
h. shape: x 2 y–intercept: (0, – 10) Roots: (1, 0) and (10, 0) Vertex: (5, 20).
i. shape: x 2 y–intercept: (0, – 7) Roots: (– 7 ,0) and (0 ,0) Vertex at (– 3, – 28)
j. shape: x 2 y–intercept: (0, – 12) Roots at (– 4, 0) and (1, 0) Vertex at (– 1, – 15)
k. shape: x 2 y–intercept: (0, 4) double zero and Vertex at (2, 0)
l. shape: x 2 y–intercept: (0, – 9) double zero and Vertex at (3, 0)
0
5
10
-2 -1 0 1 2 3 4 5 6 7 8 9 10
y x
0
10
20
-5 0 5 10 15
x
y
0
5
10
15
20
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
x
y
-16-
-8-
04
8
12
-6 -4 -2 0 2 4
y x
Using The Quadratic Formula to Sketch Graphs
Course: Principles of Economics 2 (BEA121)
University: University of Tasmania
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