Vertex Form
What is the vertex of the function f(x)=(x−3)2+5?
(3,5)
Find the vertex of the function f(x)=x2+6x+4.
(-3,-5)
What are the x-intercepts of the function f(x)=(x−2)(x+3)?
p=2, q=-3
What is the vertex of the graph? (See board)
(1,2)
Write the quadratic equation given a vertex at (2, 3) and a = 1.
f(x)=(x-2)2+3
Identify the axis of symmetry for the function f(x)=(x+1)2+2
x=-1
Identify the axis of symmetry for the function f(x)=2x2+2x+2.
x=-1/2
Identify the vertex for the function f(x)=−1(x−3)(x+5).
(-1, 16)
What are the intercepts of the function? (See the board)
p=-3, q=1
How would you write the equation given x-intercepts at 5 and -1 with a = -1? (What form would you use, why, and what is the equation?)
Use the intercept form
You're given intercepts
f(x)=-1(x-5)(x+1)
Write the equation in vertex form for the vertex at (1, -2) and a = -1.
f(x)=-1(x-1)2-2
For the function f(x)=4x2+8x+12, determine the vertex.
(-1,8)
Find the axis of symmetry for the function f(x)=(x−1)(x+3).
x=-1
Write the equation of the graph in vertex form. (See Board)
f(x)=(x-1)2+2
Write the quadratic equation from the information: vertex at (-1, -5) and a = 2.
f(x)=-2(x+1)2-5
Determine the vertex of the function f(x)=−2(x−1)2+4
(1,4)
(2, -3), x=2
Determine the vertex and axis of symmetry for the function f(x)=2(x-3)(x-5).
(4,-2), x=4
Write the equation of the graph. (See board)
f(x)=(x+3)(x-1)
Write the equation given the vertex at the origin and a = 1.
f(x)=(x-0)2+0 or f(x)=x2
For the function f(x)=(x+5)2−3, what is the vertex and axis of symmetry?
(-5,-3), x=-5
Convert the function f(x)=x2+4x+2 to vertex form.
f(x)=(x+2)2-2
For the function with intercepts at 4 and -2, write the equation in intercept form, a=1.
f(x)=(x-4)(x+2)
Analyze the graph of the function f(x)=−3(x+1)2−6 and describe its vertex and which direction it opens?
(-1,-6), Down
Given x-intercepts at 2 and 3, and a = -1, write the equation in standard form.
Intercepts Form: f(x)=-1(x-2)(x-3)
Standard Form: f(x)=-x2-5x+6