Converting Quadratic Equations

A step-by-step guide

with practice

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.

More Practice

Write this equation in intercept form: y = (x + 4)2 – 1 y = (x + 5)(x + 3)

Write this equation in vertex form: y = (x – 3)(x + 1) y = (x – 1)2 + 1