Three Forms of Quadratic
This form of a quadratic is written as
ax^2+bx+c
What is standard form?
The U-shaped graph of a quadratic function is called this.
What is a parabola?
Multiply:
(x+5)(x-3)
What is
x^2+2x-15
Factor:
x^2+7x+10
What is
(X+5)(x+2)
In y=(x-6)^2 , the graph shifts _____ 6 units.
What is right?
In a projectile motion equation, what does the vertex represent?
What is the maximum height?
This form of a quadratic is written as
a(x-h)^2+k
What is vertex form?
The highest or lowest point on a parabola.
What is the vertex?
Multiply:
(2x+3)(x-4)
What is
2x^2-5x-12
Factor:
x^2-11x+24
What is
(x-3)(x-8)
In y=(x+4)^2+3 , the graph shifts _____.
What is left 4 units and up 3 units?
What do the zeros of a projectile motion function represent?
What is when the object hits the ground?
This form of a quadratic is written as
a(x-m)(x-n)
What is factored form?
The lowest point on a parabola that opens upward.
What is the minimum?
Write in standard form:
(x-6)^2
What is
x^2-12x+36
Factor:
2x^2+6x
What is
2x(x+3)
In y=-x^2+5 , what is two transformations occur?
What is reflect over the x-axis and shift up 5 units?
Given
h(t)=-16t^2+32t+6 , what does 6 represent?
What is the starting height?
This form makes it easiest to identify the vertex.
What is vertex form?
The highest point on a parabola that opens downward.
What is the maximum?
Write in standard form:
3(x+2)(x-5)
What is
2x^2-9x-30
Factor completely:
x^2-25
What is
(x-5)(x+5)
What is the vertex of y=2(x-3)^2+1 ?
What is (3, 1)?
Using h(t)=-16t^2+32t , how long is the object in the air?
What is 2 seconds?
This form makes it easiest to identify the x-intercepts (roots/zeros).
What is factored form?
This vertical line passes through the vertex of a parabola and divides the graph into two symmetrical halves.
What is the axis of symmetry?
Convert to standard form:
(x+4)^2-7
What is
x^2+8x+9
Factor:
x^2+2x-35
What is
(x+7)(x-5)
Does y=1/2(x+2)^2 show a vertical stretch or vertical compression?
What is vertical compression?
Find the maximum height of h(t)=-16t^2+32t+8 .
What is 24 feet?
This form makes it easiest to identify the y-intercept.
What is standard form?
The root, solution, and zero of a function all describe this part of the graph where y = 0.
What is the x-intercept?
Write in standard form:
-2(x-3)^2
What is
-2x^2+12x-18
Factor:
3x^2-15x+18
What is
3(x-2)(x-3)
Describe the transformations from y=x^2 to y=-2(x-1)^2+4 .
What is shift right 1 unit, up 4 units, reflect over the x-axis, and vertical stretch of 2 units?
Which form of a quadratic makes it easiest to find maximum height?
What is vertex form?
All three forms represent the same type of function with a degree of 2.
What is a quadratic function?
A polynomial function with a degree of 2 that includes at least one term where the highest exponent is 2.
What is a quadratic function?
Write in standard form:
(2x-1)(x+5)
What is
2x^2+9x-5
Factor:
2x^2+7x-15
What is
(2x-3)(x+5)
Which equation represents a parabola with vertex (-3, 5) that opens downward?
What is y=-(x+3)^2+5
A ball is launched from a platform and modeled by h(t)=-16t^2+40t+5 . What does the vertex represent in this situation?
What is the maximum height and the time it occurs?