Quadratic Basics
What does a function need to have in order to be quadratic?
What is x2
What does vertex form of a quadratic function look like?
f(x)=a(x-h)2+k
What is the standard form of a quadratic?
f(x)=ax2+bx+c
Which is factored form of a quadratic function?
f(x)=a(x-p)(x-q)
Does the function f(x)=x2+2x+1 have a minimum or maximum?
minimum
What is the graph of a quadratic function called?
Parabola
What is the vertex
f(x)=2(x-4)2+3
(4,3)
What formula do you use to find the axis of symmetry in standard form?
-b/2a
What should you find and graph first when given a function in factored form?
The x-intercepts
How is the function f(x)=-x2 transformed?
opens downward
What is the absolute maximum or absolute minimum point on a parabola?
Vertex
Find the axis of symmetry
f(x)=-2(x+3)2+1
x=-3
What does the c-value tell you in standard form?
y-intercept
Find the axis of symmetry
f(x)=2(x-3)(x-7)
x=5
An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t2 + 19.6t + 58.8, where s is in meters.
What is the maximum height of the object?
78.4 m
Name 2 things that the a-value in standard form tell you about the shape of the parabola?
Opens up or down, narrow or wide
Find the y-value when x=2
y=2x2-3x+3
y=5
Find the axis of symmetry
f(x)=2x2+8x-3
x=-2
Find the vertex
f(x)=(x-4)(x+2)
(1,-9)
How is the function f(x)=.5x2+1 transformed?
The function is wider and moved up by 1
Which of these functions have an axis of symmetry at x=2 (could be more than 1)
a. f(x)=-2x2+8x-3
b. g(x)=(x-1)(x-5)
c. h(x)=2(x-2)2+1
a. and c.
Find the y-intercept of the function
f(x)=-2(x-1)2-1
(0,-3)
Find the vertex
f(x)=x2-4x+1
(2,-3)
Find the y-intercept
f(x)=-3(x-5)(x+3)
(0,45)
An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t2 + 19.6t + 58.8, where s is in meters.
When does the object reach its maximum height?
After 2 seconds