Equations and Graphs
T/F: The vertex of a parabola is a maximum point if the parabola opens upward.
See if each input (x) has ONLY one output (y)
f(x) = -3x2 + 5x - 9
(0, -9)
What is this equation in standard form:
f(x) = 2(x + 3)(x - 4)
f(x) = 2x2 -2x - 24
Correct this statement: The graph of the parabola with the equation: y=-2(x+3)2, opens downward, vertex at (-3, 0), and is vertically compressed by -2.
vertically stretched by 2
If you have a graph, how do you know if it represents a function? Be thorough in your explanation.
Vertical line test - see if a vertical line crosses through the graph at ONLY one point
If the Axis of Symmetry of the following parabola is at h= -5, what is the full vertex point?
f(x) = 1/2x2 + 5x - 7
(-5, -19.5)
If a parabola has a vertex at (-2, 72) and passes through (0, 64), what is the a-value of the parabola?
a = -2
Describe what this parabola looks like:
f(x) = 1/2(x + 3)2 - 8
opens up, compressed by 1/2, vertex at (-3, -8)
Is this a function? How do you know?
{(0, 1), (2, 6), (-4, -10), (2, 5), (7, -12)}
No - one input (2) has TWO outputs
What are the x-intercepts of, as points:
f(x) = (x + 2)(x - 3)
(-2, 0) (3, 0)
What is the domain of any parabola?
{xER}
Evaluate:
f(x) = 1/2x + 5 with f(6)
f(6) = 8
{yER| y>_ 10}
Evaluate:
f(x) = 3x2 + x - 1 with f(-2)
f(-2) = 9
What is the y-intercept, x-intercepts, and vertex for:
f(x) = -2x2 - 8x + 64
y: (0, 64)
x: (-8, 0)(4, 0)
v: (-2, 72)
What is the STANDARD form equation for the parabola that has x-intercepts at (-4, 0) and (10, 0) and passes through the point (0, -20)?
f(x) = 1/2x2 - 3x - 20