Graphing Quadratics from Standard Form Worksheet | Algebra

Graphing Quadratics from Standard Form Worksheet | Algebra

Graphing Quadratics from Standard Form Worksheet

Name: __________________________
Date: __________________________
Class: __________________________

Instructions

For each quadratic in standard form,

[
y=ax^2+bx+c
]

identify the key features and graph the parabola.

A. Identify the Parts

For each quadratic, identify a, b, and c.

  1. (y=x^2+4x+3)
    (a=) ______ (b=) ______ (c=) ______
  2. (y=2x^2+6x+4)
    (a=) ______ (b=) ______ (c=) ______
  3. (y=-x^2+2x+8)
    (a=) ______ (b=) ______ (c=) ______
  4. (y=3x^2-12x+9)
    (a=) ______ (b=) ______ (c=) ______
  5. (y=-2x^2-8x-6)
    (a=) ______ (b=) ______ (c=) ______

B. Find the Axis of Symmetry

Use

[
x=\frac{-b}{2a}
]

  1. (y=x^2+6x+5)
    Axis of symmetry: (x=) ______
  2. (y=x^2-8x+12)
    Axis of symmetry: (x=) ______
  3. (y=2x^2+12x+7)
    Axis of symmetry: (x=) ______
  4. (y=-x^2+10x-9)
    Axis of symmetry: (x=) ______
  5. (y=3x^2-18x+5)
    Axis of symmetry: (x=) ______

C. Find the Vertex

Find the axis of symmetry first, then substitute the (x)-value into the equation.

  1. (y=x^2+4x+3)
    Vertex: ((______, ______))
  2. (y=x^2-6x+5)
    Vertex: ((______, ______))
  3. (y=2x^2+8x+3)
    Vertex: ((______, ______))
  4. (y=-x^2+4x+5)
    Vertex: ((______, ______))
  5. (y=3x^2-12x+7)
    Vertex: ((______, ______))

D. Determine the Direction

Write opens upward or opens downward.

  1. (y=2x^2+3x-1)
  1. (y=-x^2+5x+6)
  1. (y=4x^2-8x+2)
  1. (y=-3x^2-6x+1)
  1. (y=x^2-10x+21)

E. Find the Y-Intercept

Remember: set (x=0).

  1. (y=x^2+5x+6)
    Y-intercept: __________
  2. (y=2x^2-4x+7)
    Y-intercept: __________
  3. (y=-x^2+6x-8)
    Y-intercept: __________
  4. (y=3x^2+2x-5)
    Y-intercept: __________
  5. (y=-2x^2-3x+4)
    Y-intercept: __________

F. Find the X-Intercepts

Solve each equation by factoring when possible.

  1. (y=x^2-5x+6)
    X-intercepts: __________________
  2. (y=x^2-7x+12)
    X-intercepts: __________________
  3. (y=x^2-9x+20)
    X-intercepts: __________________
  4. (y=x^2+x-6)
    X-intercepts: __________________
  5. (y=x^2-4x-5)
    X-intercepts: __________________

G. Complete the Table

Fill in the missing (y)-values.

  1. (y=x^2-4x+3)
x-1012345
y_____________________
  1. (y=-x^2+4x+5)
x01234
y_______________
  1. (y=x^2-6x+8)
x12345
y_______________

H. Graph the Quadratics

For each equation:

  • Find the vertex.
  • Find the axis of symmetry.
  • Find the y-intercept.
  • Find the x-intercepts if possible.
  • Plot the points.
  • Draw the parabola.
  1. (y=x^2-4x+3)
  2. (y=x^2-6x+8)
  3. (y=-x^2+4x+5)
  4. (y=2x^2-8x+6)
  5. (y=-2x^2+4x+6)
  6. (y=x^2+2x-8)
  7. (y=3x^2-12x+9)

I. Analyze the Graph

  1. For (y=x^2-8x+12), find:
  • Vertex: __________________
  • Axis of symmetry: __________________
  • Y-intercept: __________________
  • X-intercepts: __________________
  • Direction: __________________
  1. For (y=-x^2+6x+7), find:
  • Vertex: __________________
  • Axis of symmetry: __________________
  • Y-intercept: __________________
  • X-intercepts: __________________
  • Direction: __________________
  1. For (y=2x^2-12x+16), find:
  • Vertex: __________________
  • Axis of symmetry: __________________
  • Y-intercept: __________________
  • X-intercepts: __________________
  • Direction: __________________
  1. For (y=-2x^2-4x+6), find:
  • Vertex: __________________
  • Axis of symmetry: __________________
  • Y-intercept: __________________
  • X-intercepts: __________________
  • Direction: __________________
  1. For (y=x^2+4x-5), find:
  • Vertex: __________________
  • Axis of symmetry: __________________
  • Y-intercept: __________________
  • X-intercepts: __________________
  • Direction: __________________

Answer Key

A

  1. (a=1,\ b=4,\ c=3)
  2. (a=2,\ b=6,\ c=4)
  3. (a=-1,\ b=2,\ c=8)
  4. (a=3,\ b=-12,\ c=9)
  5. (a=-2,\ b=-8,\ c=-6)

B

  1. (x=-3)
  2. (x=4)
  3. (x=-3)
  4. (x=5)
  5. (x=3)

C

  1. ((-2,-1))
  2. ((3,-4))
  3. ((-2,-5))
  4. ((2,9))
  5. ((2,-5))

D

  1. Upward
  2. Downward
  3. Upward
  4. Downward
  5. Upward

E

  1. ((0,6))
  2. ((0,7))
  3. ((0,-8))
  4. ((0,-5))
  5. ((0,4))

F

  1. (x=2,3)
  2. (x=3,4)
  3. (x=4,5)
  4. (x=-3,2)
  5. (x=-1,5)

G

  1. y-values: 8, 3, 0, -1, 0, 3, 8
  2. y-values: 5, 8, 9, 8, 5
  3. y-values: 3, 0, -1, 0, 3

I

  • Vertex: ((4,-4))
  • Axis: (x=4)
  • Y-intercept: ((0,12))
  • X-intercepts: ((2,0),(6,0))
  • Direction: Upward
  • Vertex: ((3,16))
  • Axis: (x=3)
  • Y-intercept: ((0,7))
  • X-intercepts: ((-1,0),(7,0))
  • Direction: Downward
  • Vertex: ((3,-2))
  • Axis: (x=3)
  • Y-intercept: ((0,16))
  • X-intercepts: ((2,0),(4,0))
  • Direction: Upward
  • Vertex: ((-1,8))
  • Axis: (x=-1)
  • Y-intercept: ((0,6))
  • X-intercepts: ((-3,0),(1,0))
  • Direction: Downward
  • Vertex: ((-2,-9))
  • Axis: (x=-2)
  • Y-intercept: ((0,-5))
  • X-intercepts: ((-5,0),(1,0))
  • Direction: Upward