Standard Form
Write a quadratic equation in STANDARD FORM
y = ax2 + bx + c
What does the axis of symmetry represent on a parabola?
The vertical line that divides the parabola into two eaual halves
If a parabola opens up, does it have a minimum or maximum?
A minimum
What is the vertex of a parabola?
The highest or lowest point on the parabola
What is the vertex form of a quadratic equation?
y = a(x - h)2 + k
Identify the a, b, and c values in y = 2x2 - 5x + 7
a=2, b=-5, c=7
Find the axis of symmetry for y = x2 - 8x + 3
4
If a < 0, does the parabola have a minimum or maximum?
A maximum
Find the vertex of
y = (x - 4)2 + 1
(4,1)
Identify the vertex of
y = (x + 2)2 - 7
(-2,-7)
Which term in y = ax2 + bx + c determines whether the parabola opens up or down?
The a-value (the coefficient of x2)
Find the axis of symmetry for y = -2x2 + 4x - 1
1
Does
y = x2 - 6x + 4
have a minimum or maximum?
a = 1 > 0
The parabola has a minimum
Find the vertex of
y = x2 - 6x + 5
(3,-4)
How does
y = (x - 3)2
compare to y = x2 ?
Shifted right 3 units
What is the value of c in y = -x2 + 6x -9 and what does it represent?
c=-9 and it represents the y-intercept
The vertex is at (5,-2). What is the axis of symmetry?
x = 5
The parabola
y = -2x2 + 8x + 1
opens in which direction and why?
opens downward
Because a = -2 (negative)
Find the vertex of
y = -2x2 + 8x - 3
(2,5)
Describe the transformations from
y = x2 to y = -(x + 1)2 + 4
Left 1
Up 4
Reflected over the x-axis
In the equation y = 3x2 + 2x - 8
1. Identify the values of a, b, and c
2. State whether the parabola opens up or down
a = -3
b = 2
c = -8
opens downward
Find the axis of symmetry using the formula for
y = 3x2 + 12x + 7
-2
How can you tell if a quadratic has a minimum or maximum?
Look at the a-value
a > 0: minimum
a < 0: maximum
Name two ways to find the vertex
Use the axis of symmetry formula and substitute
Rewrite the equation in vertex form
Write a quadratic n vertex form with vertex (-2,5) that opens downward.
y = -(x + 2)2 + 5