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)

Intercept Form to Standard Form Write the equation in standard form: y = – 2(x + 3)(x – 2) y = – 2(x2 + x – 6) multiply

binomials

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

Vertex Form to Standard Form Write this equation in standard form: y = 2(x – 3)2 + 4

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 by using foil

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 by using foil

y = 2x2 – 12x + 18 + 4 distribute

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 by using foil y = 2x2 – 12x + 18 + 4 distribute y = 2x2 – 12x + 22 combine like

terms

Standard Form to Intercept Form Write the equation in intercept form: y = – 15x2 + 3x + 12

Standard Form to Intercept Form Write the equation in intercept form: y = – 15x2 + 3x + 12 y = – 3(5x2 – x – 4) common factor

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 Vertex Form Write the equation in vertex form: y = 3x2 – 6x + 8

Standard Form to Vertex Form Write the equation in vertex form: y = 3x2 – 6x + 8 y = 3(x2 – 2x ) + 8 factor out “a”

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

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

Vertex Form to Intercept Form Write the equation in intercept form: y = (x + 4)2 - 1

Vertex Form to Intercept Form

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

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 + 15combine terms

Vertex Form to Intercept Form

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

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

Intercept Form to Vertex Form

Write the equation in vertex form: y = (x – 3)(x + 1) y = x2 – 2x - 3 foil

Intercept Form to Vertex Form

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

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