Quadratics. y = x 2 Flips up because positive value Doesn’t move left or right on x axis. Stays at 0 Doesn’t move up or down y axis. Stays at 0 This is.

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Presentation transcript:

Quadratics

y = x 2 Flips up because positive value Doesn’t move left or right on x axis. Stays at 0 Doesn’t move up or down y axis. Stays at 0 This is the “parent”.

y = 1/2 x 2 Flips up because negative value Doesn’t move left or right. Stays at 0 Doesn’t move up or down. Stays at 0 Makes parabola wider

y = -4x Flips down because negative value Doesn’t move left or right. Stays at 0 Moves up 2 on y axis Makes parabola skinnier

y = 1/2 (x+3) 2 Flips up because negative value Moves left 3 on x axis Doesn’t move up or down. Stays at 0 Makes parabola wider

y = (x – 4) Flips up because positive value Moves right 4 on x axis Moves up 5 on y axis

y = -(x + 2) Flips down because negative value Moves left 2 on x axis Moves down 5 on y axis

y = - 3(x – 4) 2 + 9

y = x 2 – 7x + 12

y = (x – 3)(x + 6)

Quadratic Family Moves parent right 4 and up 5. This is the NEW vertex. x intercept: y intercept: vertex: D: R: none (0,21) (4,5) { y : y > 5}

y = x 2 – 7x + 12

HOW DO YOU FIND THE X INTERCEPTS? Set y = 0 0 = - 3(x – 4) Minus 9 from both sides. -9 = - 3(x – 4) 2 Divide by -3 3 = (x – 4) 2 Square Root both sides 1.73 = x – = x - 4 Solve. (5.73, 0) and (2.27, 0)

HOW DO YOU FIND THE X INTERCEPTS? Set y = 0 Factor OR Quadratic Formula

HOW DO YOU FIND THE VERTEX? -b 2a This gives you the X COORDINATE of the vertex. To find the y, substitute this x into the original and evaluate. OR You Could Use the Midpoint of the x intercepts.

HOW DO YOU FIND THE VERTEX? Find the midpoint of the x intercepts. Then substitute that x into the original to find it’s y coordinate.

y = (x + 8)(x - 2)

HOW DO YOU FIND THE X INTERCEPTS? Set each factor equal to 0 and solve. (Take the opposite of them.) (-8,0) and (2,0) 6 th hour ends. They need rest of this and FF1

y = (3x + 2)(5x - 2)

Quadratic Family x intercept: y intercept: vertex: D: R: (-2/3, 0) (2/5, 0) (0,-4) (-2/15, -4.27) { y : y > -4.27}

y = x 2 – 7x + 12

Quadratic Family x intercept: y intercept: vertex: D: R: (4, 0) (3, 0) (0,12) (3.5, -.25 ) { y : y > -.25}

y = x 2 + 6x + 1

Quadratic Family x intercept: y intercept: vertex: D: R: NONE (0,1) { y : y > -8} Because there are NO x intercepts YOU MUST USE –b/2a to find the VERTEX!!! (-3, -8)

x 2 – 9

4x 2 – 49

Factor (2x – 7)(2x + 7)

16x 2 – 46x + 49

Factor (4x – 7)(4x - 7)

x 2 – 7x - 18

Factor (x + 9)(x - 2)

12x 4 – 3x 3

Factor (3x 3 )(4x + 1)

(x + 10)(x - 2)

QUICK FOIL x 2 + 8x - 20

(x - 3)(x - 2)

QUICK FOIL x 2 - 5x + 6

(x – 5) 2

QUICK FOIL x x + 36

(3x + 2) 2

QUICK FOIL 9x x + 4