Vertex Form
What is the vertex?
y = (x-2)2+5
(2, 5)
What is the key feature that standard form tells you?
y=ax2+bx+c
The y-intercept: (0, c)
What are the zeros of the function y=(x-2)(x+5)?
(2, 0) and (-5, 0)
What is the graph of a quadratic function called?
A parabola
y=-3(x-7)2
Maximum
Consider the equation. y=2x2-3x+4
What is the y-intercept and does the parabola have a maximum or a minimum?
(0, 4)
Minimum
What are the zeros of the function y=(2x+7)(x-10)?
(10, 0)
(-3.5, 0)
How does the vertex relate to the zeros in a quadratic function?
The x coordinate of the vertex is the midpoint of the zeros. The y coordinate is found by plugging that x coordinate into the equation for x and solving for y.
What is the y-intercept of y=-3(x-2)2+4?
(0, -8)
True or False. If b=0, then the vertex and the y-intercept are the same point and they fall on the y-axis.
y=ax2+bx+c
True!
Write an expression equivalent to (x+3)2
x2+6x+9
Sketch a graph of y=(x-5)(x-1).
Include the zeros, the vertex, and the y-intercept.
Zeros at (5, 0) and (1, 0)
Vertex at (3, -4)
y-int at (0, 5)
Write the equation of a parabola that has a vertex of (-2, 4) and opens up (has a minimum).
Ex: y=(x+2)2+4
A projectile is shot through the air. The equation h(t)=-16t2+146t+100 models the height of the projectile over time.
Find h(2.5). What does h(2.5) represent?
H(t)=365 feet
After 2.5 seconds, the projectile is at a height of 365 feet.
Find the vertex of y=(x-4)(x-10)
(7, -9)
Sketch a graph of y=-2(x-1)2+4. Include at least 3 points.
Vertex at (1, 4)
Y-intercept at (0, 2)
Third point at (2, 2)
Sketch a graph of y=-3(x+1)2-2
Vertex at (-1, -2)
Opens Down
y-intercept at (0, -5)
Write a quadratic in standard form that opens down and has a y-intercept of (0, -0.5)
Ex: y=-2x2+4x-0.5
You have 20 meters of caution tape to mark out a rectangular area.
Write an equation for the area as a function of the width of the rectangle.
A = w(10-w)
or
A=10w-w2
Write an equation for the graph
y=(x-4)(x-2)or
y=x2-6x+8