Transcript Converting Quadratic Equations

Converting Quadratic
Equations
A step-by-step guide
with practice
Intercept Form to
Standard Form
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Write the equation in standard form:
y = – 2(x + 3)(x – 2)
Intercept Form to
Standard Form
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Write the equation in standard form:
y = – 2(x + 3)(x – 2)
y = – 2(x2 + x – 6)
multiply binomials
Intercept Form to
Standard Form
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Write the equation in standard form:
y = – 2(x + 3)(x – 2)
y = – 2(x2 + x – 6)
multiply binomials
y = – 2x2 – 2x + 12
distribute
Vertex Form to
Standard Form
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Write this equation in standard form:
y = 2(x – 3)2 + 4
Vertex Form to
Standard Form
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Write this equation in standard form:
y = 2(x – 3)2 + 4
y = 2(x2 – 6x + 9) + 4 square the binomial
by using foil
Vertex Form to
Standard Form
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Write this equation in standard form:
y = 2(x – 3)2 + 4
y = 2(x2 – 6x + 9) + 4 square the binomial
by using foil
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y = 2x2 – 12x + 18 + 4 distribute
Vertex Form to
Standard Form
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Write this equation in standard form:
y = 2(x – 3)2 + 4
y = 2(x2 – 6x + 9) + 4 square the binomial
by using foil
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y = 2x2 – 12x + 18 + 4 distribute
y = 2x2 – 12x + 22
combine like terms
Standard Form to
Intercept Form
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Write the equation in intercept form:
y = – 15x2 + 3x + 12
Standard Form to
Intercept Form
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Write the equation in intercept form:
y = – 15x2 + 3x + 12
y = – 3(5x2 – x – 4)
common factor
Standard Form to
Intercept Form
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Write the equation in intercept form:
y = – 15x2 + 3x + 12
y = – 3(5x2 – x – 4)
common factor
y = – 3(5x + 4)(x – 1) factor the trinomial
Standard Form to
Vertex Form
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Write the equation in vertex form:
y = 3x2 – 6x + 8
Standard Form to
Vertex Form
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Write the equation in vertex form:
y = 3x2 – 6x + 8
y = 3(x2 – 2x ) + 8
factor out “a”
Standard Form to
Vertex Form
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Write the equation in vertex form:
y = 3x2 – 6x + 8
y = 3(x2 – 2x ) + 8
factor out “a”
y = 3(x2 – 2x + 1) + 8 – 3
complete the
square
Standard Form to
Vertex Form
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Write the equation in vertex form:
y = 3x2 – 6x + 8
y = 3(x2 – 2x ) + 8
factor out “a”
y = 3(x2 – 2x + 1) + 8 – 3
complete the
square
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y = 3(x – 1)2 + 5
factor and
combine
Vertex Form to
Intercept Form
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Write the equation in intercept form:
y = (x + 4)2 - 1
Vertex Form to
Intercept Form
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Write the equation in intercept form:
y = (x + 4)2 - 1
y = x2 + 8x + 16 - 1
square the binomial
by using foil
Vertex Form to
Intercept Form
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Write the equation in intercept form:
y = (x + 4)2 - 1
y = x2 + 8x + 16 - 1
square the binomial
by using foil
y = x2+ 8x + 15
combine terms
Vertex Form to
Intercept Form
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Write the equation in intercept form:
y = (x + 4)2 - 1
y = x2 + 8x + 16 - 1
square the binomial
by using foil
y = x2+ 8x + 15
combine terms
y = (x + 3)(x + 5)
factor
Intercept Form to
Vertex Form
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Write the equation in vertex form:
y = (x – 3)(x + 1)
Intercept Form to
Vertex Form
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Write the equation in vertex form:
y = (x – 3)(x + 1)
y = x2 – 2x - 3
foil
Intercept Form to
Vertex Form
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Write the equation in vertex form:
y = (x – 3)(x + 1)
y = x2 – 2x - 3
foil
y = x2 – 2x - 3
get ready to
y = x2 – 2x + 1 – 3 – 1 complete the square
Intercept Form to
Vertex Form
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Write the equation in vertex form:
y = (x – 3)(x + 1)
y = x2 – 2x - 3
foil
y = x2 – 2x - 3
get ready to
y = x2 – 2x + 1 – 3 – 1 complete the square
y = (x - 1)2 - 4
factor and combine