Quadratic Graphs
How many zeros (x-intercepts) can a quadratic function have?
What is 2, 1, or none?
The value of "a" for a graph of a quadratic function opening downward.
What is negative?
The coordinates of the y-intercept for the quadratic function:
y=-2x2 + 5x - 7
What is (0,-7)?
What does it mean for a quadratic function to only have one zero? What does that curve look like?
What is it only touches the x-axis once - at the vertex
Multiply the following polynomials: (x+6)(x+9)
What is x2 + 15x +54
The shape of the graph of a quadratic function.
What is a parabola?
The vertex of the quadratic function y = 5x2 + 10x - 2 is a ____________________ point.
What is minimum?
Find the zeros (x-intercepts) of the following:
y = x2 - 8x - 20
x = 10 and x = -2
The vertex for this quadratic function:
y = (x - 4)2
What is (4, 0)?
Write an expression for the area of a square that has one side with a length of (x+4)
What is x2 + 8x + 16
The name of the line that divides a quadratic function exactly in half.
What is the axis of symmetry?
What are the roots of this quadratic function?
y = 6 (x-2)(x-8)
2 and 8
What determines whether a function will have a maximum turning point or a minimum turning point?
If the leading coefficient is positive it will be a minimum and if it is negative it will be a maximum.
Factor the following polynomial: x2 + 13x + 42
What is (x+6)(x+7)
Evaluate this function with f(-5):
f(x) = 2x3 + 15x
f(-5) = -325
The name of the point on a quadratic function that will be the maximum or minimum of the function.
What is the vertex?
Convert the quadratic function in vertex form to standard form. f(x) = -2 (x+1)2 - 5
What is -2x2 - 4x - 7
Convert the quadratic function in vertex form to standard form. f(x) = 3(x-4)2 +7
What is 3x2 - 24x +55
Convert the function that is in factored form to standard form. f(x) = -3(x-1)(x-3)
What is -3x2 +12x -9
Evaluate this function with f(7):
f(x) = -x2 + 3x
f(7) = -28
Order the following parabolas from narrowest (skinniest) to widest:
y=4x2 y=2/3 x2 y=-2x2 y= x2
What is y=2/3 x2, y= x2, y=-2x2, y=4x2
For : y = x2 - 6x + 5
a) state the x-intercepts
x = 5 and x = 1
Multiply the following polynomials: (x2 + 3x + 2) (x2 -7x +4)
What is x4 - 4x3 - 15x2 - 2x + 8
If the x-intercepts of a function are x = 6 and x=12, what is x-value of the vertex? Then, write an equation in factored form with those two x-intercepts.
x = 9
y=(x-6)(x-12)
How do you know if a table of values is a function or not?
If each input (x-value) has only one output (y-value), then it is a function