Key Features
Standard Form
Vertex Form
Graphing Calculator and Graphs
100
What are zeros?
The x-intercepts of the parabola.
100
What part of a quadratic equations tells us if the parabola has a maximum or a minimum?
The a-value:
-If positive a -> opens up, minimum
-If negative a -> opens down, maximum
100
How do you find the vertex of a parabola from a quadratic equation in vertex form?
(h,k)
100
Use your graphing calculator to make a table and graph the following quadratic function:
p(x)=2x^2-20x+50
200
Is it possible for a function to only be positive? Sketch graphs to support your answer.
Yes. Parabolas with a vertex above the x-axis and opening up.
200
What is the formula to find the axis of symmetry?
(-b)/(2a)
200
How do you find the a-value of a parabola if you are given the graph of the quadratic function?
Use the vertex of the parabola and another point on the parabola and plug those values into vertex form. Solve for a.
200
Create the vertex form of the following quadratic function.
f(x)=2(x+1)^2 -7
300
Will parabolas always have two zeros?
No - it is possible for quadratic functions to have two, one or no zeros.
Two zeros ex) parabola's vertex is below the x-axis and opens up
One zero ex) parabola's vertex is ON the x-axis
No zeros ex) parabola's vertex is below the x-axis and opens down
300
What determines the domain of a quadratic function?
All real-numbers ALWAYS
300
What value shifts the parabola left or right?
c or h
300
Use the graph to identify the features of the parabola:
vertex, max/min, zero(s), y-int, increasing, decreasing, positive, negative
vertex: (-2,6)
max @ 6
zeros: (-5, 0) and (1,0)
y-int: (0,3)
increasing: x<-2 decreasing: x>-2
positive: -5<x<1 negative: x<-5 or x>1
400
Will a parabola always have a y-intercept?
Yes. The domain is all real numbers for quadratic functions, meaning it continues left and right infinitely. This means at some point, the parabola will intersect the y-axis.
400
If the a-value of a quadratic function is less than 1 does that mean the parabola will be wider?
No. The absolute value of the value needs to be less than 1, but greater than 0. There are negative integers that could make the parabola narrower.
400
What value shifts a parabola up or down?
d or k
400
Would the graph used to model a frog jumping onto a lily pad have a domain of all real numbers? Explain.
No - the frog has a starting, maximum, and ending height. This is also over time. Both time and height cannot be measured in negative values. It will only be in Quadrant I.
500
What separates a graph from its increasing and decreasing portions.
The vertex and the axis of symmetry.
500
How do I convert a quadratic function in vertex form into standard form?
Double your set of parentheses, FOIL, multiply this product by the a-value, then add the d-value.
500
What value(s) determine the range of a quadratic function?
a -> to know if it opens up or down
d -> where the maximum or minimum value is
500
Matt compares two quadratic functions as described at the right. Which of the following statements is true?
a. g(x) has a greater max
b. h(x) has a greater max
c. g(x) has a max, h(x) has a min
d. g(x) and h(x) have the same min/max
D