Quadratic Graphs
How many zeros (x-intercepts) can a quadratic function have? List all possibilities.
2, 1, or none
What is the value of "a" for a graph of a quadratic function opening downward?
- a
What is the y - intercept?
y=-2x2 + 5x - 7
(0,-7)
Find the roots of the quadratic equation
x2-16=0
x=4, x=-4
Find the vertex of the equation x2-8x+10.
(4,-6)
What is the standard form of a quadratic equation?
ax2 + bx + c
If the a in ax2+bx+c is 0.01, is the parabola wide or narrow?
Wide
Find the zeros of the equation y=6x2-7x-5.
{5/3, -1/2}
Find the discriminant in the following equation and state the number of solutions.
f(x)=2x2-8x+5
Discriminant=24
Number of solutions= 2 real solutions
What is the positive solution of f(x) = 2x2 + 3x -2?
x=1/2
What is the name of the line that divides a quadratic function exactly in half?
Axis of Symmetry
Find the solutions of the equation x2 - 49 = 0
{7, -7}
Find the vertex form in y=-3x2-6x+6.
y=-3(x+1)2+9
Find the coordinates of the y-intercept for the quadratic function:
y=3x2 + 2x - 1
The y-intercept is (0, -1)
Get the vertex form of f(x)=x2-6x+9.
y=(x-3)2
What is the name of the point on a quadratic function that will be the maximum or minimum of the function?
vertex
What are the zeros of the equation
y = x2 + 11x + 24 ?
{-8, -3}
Find the number of solutions and the vertex for the quadratic function:
y = 4x2 + 36x + 81
Number of solutions: 1 real solution
Vertex: (-4.5,0)
Find the y-intercept and vertex for this quadratic function.
x2 + 49 = 14x
The y-intercept is (0, 49) and
the vertex is (7, 0).
f(x)=1/2(x+2)(x-10)
If the function f above has a vertex at point (h,k) in the x-y plane, what is the value of k?
k=-18
3x2+10x=8
If a and b are the two solutions to the equation above and a is greater than b, what is the value of b2?
b2= 16
What is the domain of a quadratic function?
All real numbers
y=2x2+13x-3
y+3=2(x+3)
If (x,y) is a solution of the system of equations above and x is greater than 0, what is the value of xy?
xy=2
h= 256t-16t2
A ball is thrown straight up from the ground with an initial velocity of 256 feet per second. The equation above describes the height the ball can reach in t seconds. If the ball reaches its maximum height in k seconds, what is the value of k?
k=8
Which of the following is equivalent to y=3x2-6x+10?
A)y=3x2+10
B)y=3(x-1)2+7
C)y=3(x-1)2+10
D)y=3(x+2)2-2
B)y=3(x-1)2+7