Quiz 4 – 8 1. Solve using the quadratic formula: 2. Use the descriminant ( ) to determine if there are to determine if there are 0, 1, or 2 real roots

Quiz 4 – 8Quiz 4 – 8

1. Solve using the quadratic formula:1. Solve using the quadratic formula:

2.2. Use the descriminant ( )Use the descriminant ( ) to determine if there areto determine if there are 0, 1, or 2 real roots. 0, 1, or 2 real roots.

342 xxy

a

acbbx

2

42

acb 42

522 2 xxy

4 – 10 4 – 10 Write Quadratic Functions Write Quadratic Functions and Modelsand Models

Vertex Form and Vertex Form and Intercept FormIntercept Form

RememberRemember: A function is a rule that relates: A function is a rule that relates input values (x) to output values (y). input values (x) to output values (y).

khxay 2)( ))(( qxpxay

4)2( 2 xy

6)3(2 2 xy

2)7(3 2 xy

1. Your turn1. Your turn: a = ? h = ? k = ?: a = ? h = ? k = ?

2. 2. a = ? h = ? k = ?a = ? h = ? k = ?

3. 3. a = ? h = ? k = ?a = ? h = ? k = ?)3)(2( xxy

4. 4. a = ? p = ? q = ?a = ? p = ? q = ?

5. 5. a = ? p = ? q = ?a = ? p = ? q = ?

6. 6. a = ? p = ? q = ?a = ? p = ? q = ?

)4)(1(2 xxy

)2)(3(5 xxy

TodayTodayWe are going to We are going to writewrite the quadratic equation the quadratic equation just by looking at the graph. just by looking at the graph.

You’ll get: You’ll get: (1)(1) A graphA graph(2)(2) a point on the grapha point on the graph(3)(3) either the vertex or the two x-interceptseither the vertex or the two x-intercepts

Vertex FormVertex FormVertex: (h, k) = (4, 2)Vertex: (h, k) = (4, 2)Point: (x, y) = (2, 6)Point: (x, y) = (2, 6)

(1) Did they give x-intercepts or the vertex?(1) Did they give x-intercepts or the vertex?

(2) Vertex (2) Vertex write the general write the general vertex form vertex form quadratic eq.quadratic eq.

khxay 2)(

(3) Plug given values into the equation.(3) Plug given values into the equation.

2)42(6 2 a

66 4422 22

(4) Solve for “a”.(4) Solve for “a”. 2)2(6 2 a 246 a1a

(5) Write the (5) Write the specificspecific vertex form equation for this graph. vertex form equation for this graph.

2)4( 2 xy

Vertex FormVertex FormVertex: (-3, -1)Vertex: (-3, -1)Point: (x, y) = (-5, -9)Point: (x, y) = (-5, -9)



khxay 2)(


1))3(5(9 2 a

-9-9 -3-3-5-5 -1-1

(4) Solve for “a”.(4) Solve for “a”. 1)2(9 2 a a482a


1)3(2 2 xy

Your turn: Your turn: 7. 7. Find the equationFind the equation

Vertex: (-4, -2)Vertex: (-4, -2)Point: (x, y) = (-3, 0)Point: (x, y) = (-3, 0)



khxay 2)(


2))4(3(0 2 a00 -4-4-3-3 -2-2

(4) Solve for “a”.(4) Solve for “a”. 2)1(0 2 a 2a


2)4(2 2 xy


Vertex: (3, -1)Vertex: (3, -1)Point: (x, y) = (2, -4)Point: (x, y) = (2, -4)



khxay 2)(


1)32(4 2 a

-4-4 3322 -1-1

(4) Solve for “a”.(4) Solve for “a”. 1)1(4 2 a 3a


1)3(3 2 xy

Intercept FormIntercept Form x-intercepts: 4, 1x-intercepts: 4, 1Point: (x, y) = (3, -4)Point: (x, y) = (3, -4)


(2) x-intercepts (2) x-intercepts write the general write the general intercept form intercept form quadratic eq.quadratic eq.


)13)(43(4 a

-4-4 4433 11

(4) Solve for “a”.(4) Solve for “a”. )2)(1(4 a a24 2a

(5) Write the (5) Write the specificspecific intercept form equation for this graph. intercept form equation for this graph.

)1)(4(2 xxy

))(( qxpxay

33

x-intercepts: -2, -4x-intercepts: -2, -4Point: (x, y) = (-5, -9)Point: (x, y) = (-5, -9)


(2) x-intercepts (2) x-intercepts write the general write the general intercept form intercept form quadratic eq.quadratic eq.


)45)(25(9 a

-9-9 -2-2-5-5 -4-4

(4) Solve for “a”.(4) Solve for “a”. )1)(3(9 a a393a


)4)(2(3 xxy

))(( qxpxay

-5-5



(2) Both (2) Both write the general write the general intercept form intercept form quadratic eq.quadratic eq.


)64)(24(4 a

-4-4 2244 66

(4) Solve for “a”.(4) Solve for “a”. )2)(2(4 a a44 1a


)6)(2( xxy

))(( qxpxay

44

Your turn: Your turn: 10. 10. Find the equationFind the equation in in intercept formintercept form..

(2, 0)(2, 0)

(6, 0)(6, 0)

(4, -4)(4, -4)

What if:What if:They wanted the final equation in They wanted the final equation in standard formstandard form??

(1)(1) Find Find eithereither vertex or intercept form (depending vertex or intercept form (depending on whether they gave a vertex or intercepts.on whether they gave a vertex or intercepts.

)6)(2( xxy

(2) Simplify (multiply and combine like terms) to (2) Simplify (multiply and combine like terms) to convert to standard form. convert to standard form.

1282 xxy

)6)(2( xxy

Your turn: Your turn: ConvertConvert the following equations to the following equations to standard formstandard form..

11.11.

12.12. )2)(3(2 xxy

13.13. 1)3( 2 xy

13.13. 6)2(5 2 xy

Your Turn:Your Turn: khxaxf )(

14.14.

15.15.

16.16.

Find the Find the slope of the right sideslope of the right side and and vertexvertex of each graph. of each graph.

574)( xxf

532)( xxf

6)( xxf

Your turn:Your turn:

y = f(x + 3) – 4 y = f(x + 3) – 4

((00, 0), 0) x x -- 33 ((-3-3, 0), 0)(-3, (-3, 00)) y – 4y – 4 (-3, (-3, -4-4))

khxfay )(*stretchstretch

shiftshift

shiftshift

28. 28. f(x): (0, 0)f(x): (0, 0)

((22, 3), 3) 22 ++ 11 ((33, 3), 3)((33, , 33)) 3 + 23 + 2 ((33, , 55))

Apply the given transformation to the point. Apply the given transformation to the point.

29. 29. g(x): (2, 3)g(x): (2, 3) y = f(x – 1) + 2 y = f(x – 1) + 2

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Quiz 4 – 8 1. Solve using the quadratic formula: 2. Use the descriminant ( ) to determine if there are to determine if there are 0, 1, or 2 real roots