Converting Quadratic Equations A stepbystep guide with practice

Converting Quadratic Equations A step-by-step guide with practice

Intercept Form to Standard Form l l 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 l l l Write the equation in standard form: y = – 2(x + 3)(x – 2) y = – 2(x 2 + x – 6) multiply binomials If you need a hint …go to next slide to see next step.

Intercept Form to Standard Form l l Write the equation in standard form: y = – 2(x + 3)(x – 2) y = – 2(x 2 + x – 6) multiply binomials y = – 2 x 2 – 2 x + 12 distribute

Intercept Form to Standard Form l Try these: y = 3(x + 1)(x + 2) l y = ½ (2 x + 3)(x – 2) l Check your answers on the next slide.

Intercept Form to Standard Form l l l Try these: y = 3(x + 1)(x + 2) y = 3 x 2 + 9 x + 6 y = ½ (2 x + 3)(x – 2) y = x 2 – ½ x – 3

Vertex Form to Standard Form l l 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 l l l Write this equation in standard form: y = 2(x – 3)2 + 4 y = 2(x 2 – 6 x + 9) + 4 square the binomial If you need a hint …go to next slide to see next step.

Vertex Form to Standard Form l l Write this equation in standard form: y = 2(x – 3)2 + 4 y = 2(x 2 – 6 x + 9) + 4 square the binomial y = 2 x 2 – 12 x + 18 + 4 distribute If you need a hint …go to next slide to see next step.

Vertex Form to Standard Form l l l Write this equation in standard form: y = 2(x – 3)2 + 4 y = 2(x 2 – 6 x + 9) + 4 square the binomial y = 2 x 2 – 12 x + 18 + 4 distribute y = 2 x 2 – 12 x + 22 combine like terms

Vertex Form to Standard Form l Try these: y = 3(x + 1)2 – 5 l y = – (x + 3)2 – 2 l Check your answers on the next slide.

Vertex Form to Standard Form l l l Try these: y = 3(x + 1)2 – 5 y = 3 x 2 + 6 x – 2 y = – (x + 3)2 – 2 y = – x 2 – 6 x – 11

Standard Form to Intercept Form l l Write the equation in intercept form: y = – 15 x 2 + 3 x + 12 If you need a hint …go to next slide to see next step.

Standard Form to Intercept Form l l l Write the equation in intercept form: y = – 15 x 2 + 3 x + 12 y = – 3(5 x 2 – x – 4) common factor If you need a hint …go to next slide to see next step.

Standard Form to Intercept Form l l Write the equation in intercept form: y = – 15 x 2 + 3 x + 12 y = – 3(5 x 2 – x – 4) common factor y = – 3(5 x + 4)(x – 1) factor the trinomial

Standard Form to Intercept Form l Try these: y = x 2 – 12 x + 32 l y = 5 x 2 – 25 x + 30 l Check your answers on the next slide.

Standard Form to Intercept Form l Try these: y = x 2 – 12 x + 32 y = (x – 8)(x – 4) l y = 5 x 2 – 25 x + 30 l y = 5(x – 2)(x – 3) l l

Standard Form to Vertex Form l l Write the equation in vertex form: y = 3 x 2 – 6 x + 8 If you need a hint …go to next slide to see next step.

Standard Form to Vertex Form l l l Write the equation in vertex form: y = 3 x 2 – 6 x + 8 y = 3(x 2 – 2 x ) + 8 factor out “a” If you need a hint …go to next slide to see next step.

Standard Form to Vertex Form l l Write the equation in vertex form: y = 3 x 2 – 6 x + 8 y = 3(x 2 – 2 x ) + 8 factor out “a” y = 3(x 2 – 2 x + 1) + 8 – 3 complete the square If you need a hint …go to next slide to see next step.

Standard Form to Vertex Form l l Write the equation in vertex form: y = 3 x 2 – 6 x + 8 y = 3(x 2 – 2 x ) + 8 factor out “a” y = 3(x 2 – 2 x + 1) + 8 – 3 complete the square l y = 3(x – 1)2 + 5 factor and combine

Standard Form to Vertex Form l Try these: y = x 2 – 4 x + 10 l y = – 2 x 2 – 4 x + 1 l Check your answers on the next slide.

Standard Form to Vertex Form l l l Try these: y = x 2 – 4 x + 10 y = (x – 2)2 + 6 y = – 2 x 2 – 4 x + 1 y = – 2(x + 1)2 + 3

More Practice l l 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 l l l 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