UNIT 2 – QUADRATIC RELATIONS & EQUATIONS
MA40: ALGEBRA 2
Task #2b – The Shot Put Problem (Solidify Understanding)
Name:
Common Core: HS.F.IF.7.a
Period:
Objective: Determine the vertex, axis of symmetry, domain, range, vertical and horizontal intercepts.
I.
A.
Independent & Dependent Variables
Definitions
1. Independent Variable – the input variable / x-value
2. Dependent Variable – the output variable / y-value
B.
Identify the independent and dependent variables. What does the variable
represent.
1. Given the equation Pz   3z 2  14 z  5, where Pz  represents the
number of flubbers given there are z tubblers.
2.
3.
II.
The table below gives the stopping distance for an automobile under
certain road conditions.
Speed (mi/h)
20
30
40
50
55
Stopping Distance (ft)
17
38
67
105
127
A company knows that  2.5 p  500 models the number it sells per month
of a certain make of unicycle, where the price p can be set as low as $70
or as high as $120. Revenue from sales is the product of the price and the
number sold.
Calculator: Find the Value of a Function
The equation Pt   x 2  77 x  410 is the price of production after t days.
i) What is the price of production after 72 days?
ii) We are in the 21st day of production. What is the price?
iii) State the price of production on the 61st day.
Task #2b – The Shot Put Problem (continued)
III. Vertical Intercepts (y-intercepts)
A. Definition
Vertical Intercept – is the point the graph intersects the y-axis. Represented by
the ordered pair 0, y .
B. Find the y-intercept using the fact that x  0 on the y-axis.
1. y  0.132 x 2  0.5x  13
2. f x   32 x 2  15 x  4
C. Find the y-intercept of a quadratic equation in the form y  ax 2  bx  c. Use the
fact that the y-coordinate of the y-intercept equals the constant term of the
function.
1. y  2.13x 2  0.125 x  1.8
2. f x    x 2  2 x  5
D. Use your calculator and the fact that x  0 is the x-coordinate of the y-intercept to
find the vertical intercept of the function.
1.
y  0.032 x 2  0.5 x  25
2.
f x  
2 2
x  x  11
3
IV. Horizontal Intercepts (x-intercepts)
A. Definition
Horizontal Intercept – is the point the graph intersects the x-axis. Represented by
the ordered pair x,0.
Zero – the “zero” of a function is the x-value of the x-intercept.
B. Find the horizontal intercept(s) of the functions using a calculator feature.
1. y  2 x 2  20 x  42
2. f x   2 x 2  .701x  3.916
Task #2b – The Shot Put Problem (continued)
V. Vertex of a Parabola
A. Definition
Vertex of a Parabola – is the highest or lowest point of a parabola.
Formula for Finding Vertex of a Parabola:
The vertex can be written as h, k  where h 
b
and k  f h.
2a
B. Find the vertex of the quadratic equation by finding the values of h and k .
1. y  2 x 2  20 x  42
2. f x    x 2  2 x  5
C. Find the vertex of the quadratic equation using a feature of your calculator.
1. y  4 x 2  12 x  9
2. f x   6 x 2  12 x  1
VI. Axis of Symmetry
A. Definition
Axis of Symmetry – of a parabola is a vertical line through the vertex.
B. Find the axis of symmetry for the following quadratic equations.
1. y   x 2  3x  6
2. f x   2 x 2  4 x
Task #2b – The Shot Put Problem (continued)
VII. Forms of Quadratic Equations
A. Definitions
Standard Form of Quadratic Equation: y  ax 2  bx  c
where the vertex h, k  can be found using h 
b
and k  f h.
2a
Vertex Form of Quadratic Equation: y  a x  h   k
2
where the vertex h, k  can be found directly from the equation.
B. Rewrite the quadratic equation from standard form to vertex form. Find h and k
using the equation above. Then substitute them directly into the vertex form. Do
not simplify.
1. y  x 2  4 x  1
2. f x   3x 2  12 x  10
C. Rewrite the quadratic equation from vertex form to standard form by simplifying
the equation. To simplify, use PEMDAS.
2
1. y  3 x  5  7
2. f x   2x  32  1
D. What is the vertex of the quadratic equation?
2
1. y  3 x  5  7
2.
f x   2 x  3  1
2
E. Find the quadratic equation in vertex form given a and the vertex h, k .
1. a  7, vertex  3,4
2. a 
2
, vertex 2,6
3