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Graphing Graphing Quadratic Quadratic FunctionsFunctions
2 Forms of Quadratic Equations
y = ax2 + bx + c
y = a(x – h)2 + kStandard
FormVertex Form
The axis of symmetry for the parabola is the vertical line through the vertex.
Graphing Using Vertex Form
y = a(x – h)2 + k
Vertex: (h, k)
Axis of symmetry: x = h
VERTICAL LINEIf a is positive, then it opens up.
If a is negative, then it opens down.
Graphing Using Vertex Form
1.Find and sketch the axis of symmetry (opposite of h).
2.Find and plot your vertex (opposite of h, same as k).
3.Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value)
Graphing Using Vertex Form
4. Use Symmetry to plot the points on the opposite side of your axis of symmetry.
5. Connect them with a U-shaped curve
Tell whether it opens up or down, axis of symmetry, and name the vertex.
f(x)= -3(x – 2)2 + 5
Vertex: (2, 5)
Axis of symmetry: x = 2
Opens DOWN
a = -3
h = 2 k = 5
y = a(x – h)2 + k.
f(x) = (x + 4)2 – 6a = 1 h = -4 k = -6
Tell whether it opens up or down, axis of symmetry, and name the vertex.
Vertex: (-4, -6)
Axis of symmetry: x = -4Opens UP
You try…
x 2(x + 5)2 - 4
y (x, y)
2f 2( 5) 4x x
Graph
x y (x, y)
21f ( 3) 1
2x x
Graph
21( 3) 1
2x
Graphing Using Standard Form
*Once it is in standard form:1.Find and sketch the axis of symmetry using 2.Find your vertex by substituting your axis of symmetry back into the original equation and solve for y.
a
bx
2
Graphing Using Standard Form
4. Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value)
5. Use Symmetry to plot the points on the opposite side of your axis of symmetry.
6. Connect them with a U-shaped curve
*Remember: If a is positive, it opens up, if a is negative, it opens down.
x (x)2 + 8x + 13
y (x, y)
2f 8 13x x x
x b2a
Graph
x -(x)2 + 2x y (x, y)
2f 2x x x
x b2a
Graph
Converting From Converting From Vertex Form to Vertex Form to Standard Form:Standard Form:y = (x – 3)2 + 5
Step 1: FOIL the binomialStep 2: Multiply the “a” term
by what you just foiledStep 3: combine like terms!
Convert the following to Convert the following to standard form:standard form:
y = 2(x – 4)2 + 6
Convert the following to Convert the following to standard form:standard form:
y = (x + 3)² + 4
Step 1: Identify a, b, and cStep 2: find the vertex (h, k)
x-coordinate (h) =
y-coordinate (k) = substitute the value you found for the x coordinate.
Step 3: Substitute a, h, and k into vertex form!
2
ba
Converting From Converting From Standard Form to Standard Form to
Vertex FormVertex Form
Convert the following to vertex form:Convert the following to vertex form:
What is the vertex form of a What is the vertex form of a parabola whose standard parabola whose standard form equation is:form equation is:
Convert the following to vertex form:Convert the following to vertex form: