Complete the table and graph x (x - 3) Vertex

1.y = ax 2 + bx + c 2.y = a(x – h) 2 + k 3. y = -2x 2 - 8x y = (x – 2) y = (x + 9) 2 6. y = ½x 2 + 6x + 5

7. y = x 2 + 2x y = x 2 – 8 9.y = 2x 2 + x10.y = -2x 2 + 8x + 3

11. y = -(3x – 4) y = 2x(x + 7) y = 4(x – 1) y = (x + 1) 2 – 7

15.Direction: Opens Up Width: Wide AOS: x = 2 Vertex: (2, -1); Minimum y – intercept: (0, 0) # of Real Solutions: 2 x – intercept: (4, 0) & (0, 0) Function? Yes Domain: (- ,  ) Range: [-1,  ) Rising: (2,  ) Falling: ( , 2) x¼(x – 2) 2 – ¾ 2 3- ¾ 40

Need Help? Look in textbook in Section 5.3: Translating Parabolas Worksheet: Properties of Parabolas in Vertex Form

Day 18: Translating Parabolas

Objectives: Use vertex form to identify properties of parabolas

What is vertex form?

Direction: Parabolas open up or open down Direction is determined by the sign of “a” Open “up” a is positive Open “down” a is negative y = a(x - h) 2 + k

Width: Parabolas can be narrow, standard or wide Width is determined by the value of a (not including the sign) Narrow |a| > 1 Standard |a| = 1 Wide |a| < 1 y = a(x - h) 2 + k

Axis of Symmetry: The line that divides the parabola into two parts that are mirror images AOS is found using: Vertex: The point where the parabola passes through the AOS Vertex is found by using: Equation: a = 2, h = -1, k = -4 AOS: x = – 1 Vertex: (-1, -4) Vertex is a minimum y = a(x - h) 2 + k

y – intercept: The point on the graph where the parabola intersects the y-axis. y – intercept is found by, making x = 0 and solving for y Y – intercept will NOT the be “c” value as it is in standard form Equation: y -intercept: (0, -2) y = a(x - h) 2 + k

Number of Real Solutions: The number of times the parabola intersects the x-axis on the real coordinate plane. Use the direction and the vertex to determine the number of real solutions Picture the direction Picture the vertex on the graph How many times will the parabola intersect the x-axis? y = a(x - h) 2 + k

x – intercept(s): The point(s) on the graph where the parabola intersect the x - axis. Other names include: roots, zeroes and solutions. To find x – intercepts, make y = 0 and solve. Solve using square roots in vertex form. y = a(x - h) 2 + k Equation: x -intercept: (-1- √2, 0 ) & (-1+ √2, 0 )

Operates the same in vertex and standard form: Function?: always passes VLT Domain: always (- ,  ) Range: Depends on vertex and direction Intervals of Rising: Depends on vertex and direction Intervals of Falling: Depends on vertex and direction

Direction: _____________ Width: ______________ AOS: _________________ Vertex: _______________ Max or Min? __________ y – int: _____________ # of Real Solutions: ______ x – int: _____________ Function? __________ Domain: ___________ Range: _____________ Rising: _____________ Falling: ____________ Opens Up Standard x = -7 (-7, 0) Minimum (0, 49) Yes (- ,  ) [0,  ) (-7,  ) (- , -7) a is positive a =1 1

Direction: _____________ Width: ______________ AOS: _________________ Vertex: _______________ Max or Min? __________ y – int: _____________ # of Real Solutions: ______ x – int: _____________ Function? __________ Domain: ___________ Range: _____________ Rising: _____________ Falling: ____________ Opens Down Wide/Stretched x = 6 (6, 3) Maximum (0, -9) Yes (- ,  ) (- , 3] (- , 6) (6,  ) a is negative a =1/3 2

Name two properties you have to calculate differently in vertex form compared to standard form.