Show:
Function Compositions
Quadratic Basics
Graph Features
Intercepts, Domain & Range
Vertex Form
100

f(x)=x2−3 and g(x)=x,

 find f(g(x)).

x-3

100

Identify a,b,c for y=2x2−3x+5.

a=2,b=−3,c=5

100

Find the y-intercept of y=x2−5x+4.

(0, 4)

100

State the domain of y=x2−4x+3

(−∞,∞)

100

Rewrite y=x2−6x+11 in vertex form.

y=(x−3)2+2

200

f(x)=x2−3; g(x)=x

Find g(f(x))

g(f(x))=√(x2−3)

200

Does the parabola y=−3x2+4x−1y=−3x2+4x−1 open up or down?Why?

Down (since a=−3)

200

Find the x-intercepts of y=x2−9.

x=±3

200

Find the range of y=(x−4)2−9.

y≥−9

200

Write the vertex form of a parabola with vertex (2, –5) and a=1.

y=(x−2)2−5

300

f(x)=x2−3; g(x)=x

Write the function f∘g(x)f∘g(x) and state its domain.

f∘g(x)=x−3, domain: x≥0

300

Find the vertex of y=(x−2)2+7.

(2, 7)

300

Given y=−x2+6x−5, find the vertex.

x=3, y=4 → Vertex (3, 4)

300

Find the x-intercepts of y=2x2−8x+6

y=2(x2−4x+3)

→2(x−1)(x−3)

→x=1,3

300

Convert y=3x2−12x+8 to vertex form.

y=3(x−2)2−4

400

f(x)=x2−3; g(x)=x

Write the function g∘f(x) and state its domain.

g∘f(x)=√(x2−3), 

domain: x2−3≥0

⇒x≤−√3 or x≥3

400

Find the vertex and axis of symmetry of y=2x2−8x+3.

Vertex (2, –5), Axis x=2x=2

400

Sketch a quick graph of y=(x+2)2−3 showing vertex and intercepts.

Vertex (–2, –3), opens up, y-int = 1

400

Determine the range of y=−x2+2x+3

Vertex (1, 4) → y≤4


400

For y=−2(x+3)2+1, list vertex, direction, and range.

Vertex (–3, 1), opens down, y≤1

500

f(x)=x2−3; g(x)=x

Evaluate f(g(16))

g(16)=4,

 f(4)=42−3

=13

500

Write the equation of a parabola that opens down, has vertex (1, –2), and passes through (3, –10).

Plug in: y=a(x−1)2−2;
  –10 = a(3–1)² – 2 

 → –10 = 4a – 2 

→ a = –2 

→ y=−2(x−1)2−2

500

A parabola has vertex (1, –4) and passes through the point (3, 0). Write the equation of this parabola in vertex form.

Use y=a(x−1)2−4, plug in (3, 0):
0=a(3−1)2−4

⇒a=10

=a(3−1)2−4

⇒a=1
Equation: y=(x−1)2−4

500

Compare the graphs of y=x2+2 and y=−x2+2. State the vertex and range of each, then describe one difference between them.

  • For y=x2+2: Vertex (0, 2), opens up, range y≥2

  • For y=−x2+2: Vertex (0, 2), opens down, range y≤2

  •  Difference: Same vertex, opposite directions; one has a minimum, the other has a maximum.


500

Find the axis of symmetry and vertex of y=−x2−4x−3 without completing the square.

x=−b/2a=−2, y=1 → Vertex (–2, 1)