What's the Vertex?
y = x^2
(0,0)
y = x^2
x =0
y = (x + 2)^2 - 4
All real numbers > or equal to -4
What are the x-intercepts?
5 and -4
How man x-intercepts does the graph of y = x^2 + 9x + 20 have, and how do you know?
2 b/c using zpp on the factored form y = (x + 4)(x + 5) generates 2 x-intercepts of -4 and -5
y = 4x^2 +7
(0,7)
y = (x+1)^2 - 25
x = -1
Y = -2(x + 3)^2 -7
All real numbers < or equal to -7
Is this parabola wider or narrower than y = x^2 and how do you know?
narrower because the absolute value of the leading coefficient is more than 1
The height of a ball above the ground after t seconds after it is thrown is h(t) = -16t^2+32t+20. How high does the ball go?
What is 36 ft
y = 2x^2 +16x-1
(-4, -33)
y = x^2- 8x+1
x=4
y = 0.5(x - 3)^2 +6
All real numbers > or equal to 6
What is the y intercept and how do you know?
40 b/c when x = 0, y = 40.
How many x-intercepts does the graph of y = x^2 +1 have, and why?
none, b/c the graph opens up, the AOS is x = 0, and the vertex is (0, 1), so the entire graph is above the x-axis
y = -3x^2+18x-3
(3,14)
y = 2x^2 - 6x+3
x = 1.5
y = -3x^2 + 18x - 3
all real numbers < or equal to 14
What is the vertex and equation of the axis of symmetry?
.5, 40.5) and x = .5
Give an example of a quadratic equation that opens up, is narrower than the parent function and has a y intercept of -8.
What is y = 2x^2 - 8
y = (x-2)^2+7
(2,7)
y = 4x^2 - 4x - 3
x = 0.5
y = 100x^2 -100
All real numbers > or equal to -100
What is the domain and range
Domain is all real numbers
Range is all real numbers < or equal to 40.5
Give an example of a quadratic function that opens down, is the same width of the y = x^2, and has an axis of symmetry of x = -5
y = -x^2 - 10x + 3