Quadratic Graphs
What is the value of "a" for a graph of a quadratic function opening downward.
"a" is negative
The "c" value in standard form tells you which component of the graph?
y-intercept
What is the y-intercept for the quadratic function?:
y=-2x2 + 5x - 7
What is (0,-7)?
If the x-intercepts of a function are x = 6 and x=12, what is the Axis of Symmetry (x-value of the vertex)?
x = 9
The y component of the vertex can be found by plugging the _______ back into the original quadratic equation.
Axis of symmetry (x)
What determines whether a function will have a maximum turning point or a minimum turning point?
Whether or not the highest power term is negative.
Is the vertex of the quadratic function y = 5x2 + 10x - 2 a maximum or minimum point?
It's a minimum
Find the zeros (x-intercepts) of the following:
y= 3 (x-6)(x+4)
x= -4 and x= 6
The vertex for this quadratic function:
y = 5(x-2)(x-6)
(4,-20)
Find the equation of a quadratic in vertex form through the point (-1,3) and has a vertex of (-2,6)?
y= -3(x+2)2 + 6
What is the name of the line that divides a quadratic function exactly in half?
The axis of symmetry
Given a point and the vertex, use the _____ form of a quadratic equation.
Vertex
Find the zeros (x-intercepts) of the following:
y = x(x-10)
x =0 and x=10
Find the y-intercept and vertex for this quadratic function (round to nearest tenth).
y = -4.9x2 +16.4x + 1
The y-intercept (0, 1) and
the vertex (1.7, 14.7)
Find the equation of a quadratic in intercept form through the point (14,4) and has x-intercepts (9,0) and (1,0).
y= .06 (x-9)(x-1)
What is the name of the point on a quadratic function that will be the maximum or minimum of the function?
The vertex?
Given the x-intercepts and another point, use the _____ form of a quadratic equation.
Intercept
Find the vertex for the quadratic function:
y = x2 + 10x + 6
What is (-5, -19)
Find the max/min value and find the domain and range of the function:
y= -2x2 + 8x + 7
Max @ (2,15). Max value is 15.
Domain: All real #s
Range: (-Infinity, 15]
A grasshopper can jump incredible distances, up to 20 times its length. The height (in inches) of the jump above the ground of a 1-inch-long grasshopper is given by, h(x)= (-1/20)x2 +x, where x is the horizontal distance (in inches) of the jump. How far does the grasshopper jump? How high does the grasshopper jump?
Jumps 20 ft away, and 5 ft high.
How many zeros (x-intercepts) can a quadratic function have? List all possibilities.
2, 1, or none
Given 3 points, solve for a quadratic equation using ______. The equation found will be in _______ form.
1. Systems of equations
2. Standard
The vertex for this quadratic function is?:
y = 2(x-2)2 - 3
What is (2, -3)?
On what intervals does the following function increase/decrease?
y= (1/4)x2 - 3x+2
Decreasing: (- Infinity, 6)
Increasing: (6, Infinity)
Analyze the differences to determine whether the
data is quadratic. If so, write an equation to model
the quadratic function.
(1,39), (2,60), (3,75)
-3x2+30x+12