Parabolas
What is a parabola?
A graph formed by a quadratic equation.
Please Factor x2 + 3x + 2
(x + 2)(x+1)
Please find the y - intercept of x2 + 2x + 3
3
What is a vertex?
The minimum or maximum point of a graph or parabola
What is the value of x:
3x + 1 = 0
x = -1/3
Name three parts of a parabola.
Roots/zeros/x-intercepts
y-intercept
vertex
Please Factor x2 + 8x + 12
(x + 2)(x+6)
Please find the y-intercept of 2x2 - 4x
0
If the x-intercepts of a parabola are (-3, 0) and (-1, 0), what is the x-value of the vertex?
-2
What are the values of x:
(x + 2)(x - 2) = 0
x = -2, x = 2
How do you find the y-intercept of a parabola?
Set x = 0 and Solve
Find the "c" value
Please factor x2 + 2x - 24
(x - 4)(x + 6)
Please find the y-intercept of x2 - 4
-4
If the vertex has an x-value of -2, what is the y-value if the equation is x2 + 4x + 3?
-1
(x + 2)(x + 2) = 0
x = -2
How do you find the x-intercept(s) of a parabola algebraically?
1. Find the quadratic equation
2. Factor or use the quadratic formula
3. Use the Zero-Product Property if necessary
Please factor 3x + 2x + 5
(3x + 1)(x - 1)
Please find the x-intercepts of x2 + 4
(-2, 0) and (2, 0)
What is the vertex of a parabola described by the equation x2 + 2x -3?
(-1, -4)
What are the values of x:
(3x + 1)(x+2) = 0
x = -2, x=-1/3
How do you find the vertex of a parabola?
1. Find x-intercepts
2. Average intercepts
3. Plug-in found x-value to find y-value
Alternatively: Use Equation, plug value in to find y-value
Please factor x2 - 4
(x + 2)(x - 2)
Please find the x-intercepts of x2 + 3x + 2
(-2, 0) and (-1, 0)
What is the vertex of a parabola described by the equation x2 + 4x -5?
(-2, -9)
Please use the Zero-Product Property to find the x-intercepts of 3x2 + 2x -1
x = -1/3, x = 1