Converting Quadratic Equations
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Transcript of Converting Quadratic Equations
Intercept Form to Standard Form
Write the equation in standard form: y = – 2(x + 3)(x – 2)
If you need a hint …go to next slide to see next step.
Intercept Form to Standard Form
Write the equation in standard form: y = – 2(x + 3)(x – 2) y = – 2(x2 + x – 6) multiply
binomials
If you need a hint …go to next slide to see next step.
Intercept Form to Standard Form
Write the equation in standard form: y = – 2(x + 3)(x – 2) y = – 2(x2 + x – 6) multiply
binomials y = – 2x2 – 2x + 12 distribute
Intercept Form to Standard Form
Try these: y = 3(x + 1)(x + 2)
y = ½ (2x + 3)(x – 2)
Check your answers on the next slide.
Intercept Form to Standard Form
Try these: y = 3(x + 1)(x + 2) y = 3x2 + 9x + 6
y = ½ (2x + 3)(x – 2) y = x2 – ½ x – 3
Vertex Form to Standard Form
Write this equation in standard form: y = 2(x – 3)2 + 4
If you need a hint …go to next slide to see next step.
Vertex Form to Standard Form
Write this equation in standard form: y = 2(x – 3)2 + 4 y = 2(x2 – 6x + 9) + 4 square the
binomial
If you need a hint …go to next slide to see next step.
Vertex Form to Standard Form
Write this equation in standard form: y = 2(x – 3)2 + 4 y = 2(x2 – 6x + 9) + 4 square the
binomial y = 2x2 – 12x + 18 + 4 distribute
If you need a hint …go to next slide to see next step.
Vertex Form to Standard Form
Write this equation in standard form: y = 2(x – 3)2 + 4 y = 2(x2 – 6x + 9) + 4 square the
binomial y = 2x2 – 12x + 18 + 4 distribute y = 2x2 – 12x + 22 combine like
terms
Vertex Form to Standard Form
Try these: y = 3(x + 1)2 – 5
y = – (x + 3)2 – 2
Check your answers on the next slide.
Vertex Form to Standard Form
Try these: y = 3(x + 1)2 – 5 y = 3x2 + 6x – 2
y = – (x + 3)2 – 2 y = – x2 – 6x – 11
Standard Form to Intercept Form
Write the equation in intercept form: y = – 15x2 + 3x + 12
If you need a hint …go to next slide to see next step.
Standard Form to Intercept Form
Write the equation in intercept form: y = – 15x2 + 3x + 12 y = – 3(5x2 – x – 4) common factor
If you need a hint …go to next slide to see next step.
Standard Form to Intercept Form
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 Intercept Form
Try these: y = x2 – 12x + 32
y = 5x2 – 25x + 30
Check your answers on the next slide.
Standard Form to Intercept Form
Try these: y = x2 – 12x + 32 y = (x – 8)(x – 4)
y = 5x2 – 25x + 30 y = 5(x – 2)(x – 3)
Standard Form to Vertex Form
Write the equation in vertex form: y = 3x2 – 6x + 8
If you need a hint …go to next slide to see next step.
Standard Form to Vertex Form
Write the equation in vertex form: y = 3x2 – 6x + 8 y = 3(x2 – 2x ) + 8 factor out “a”
If you need a hint …go to next slide to see next step.
Standard Form to Vertex Form
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
If you need a hint …go to next slide to see next step.
Standard Form to Vertex Form
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 y = 3(x – 1)2 + 5 factor and
combine
Standard Form to Vertex Form
Try these: y = x2 – 4x + 10
y = – 2x2 – 4x + 1
Check your answers on the next slide.
Standard Form to Vertex Form
Try these: y = x2 – 4x + 10 y = (x – 2)2 + 6
y = – 2x2 – 4x + 1 y = – 2(x + 1)2 + 3
More Practice
Write this equation in intercept form: y = (x + 4)2 – 1
Write this equation in vertex form: y = (x – 3)(x + 1)
Check your answers on the next slide.