 # Graphing and Solving. a)What do they look like? b)How can you tell a function is quadratic? c)What are some terms associated with quadratic functions?

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Graphing and Solving

a)What do they look like? b)How can you tell a function is quadratic? c)What are some terms associated with quadratic functions? vertex, x and y intercept(s),axis of symmetry, max/min, domain/range d)Evaluate f(x) = 2x 2 + 3x – 5 when x = -2 both with and without a calculator. f(x) = -3

Graph using a table of values. Determine whether the function has a maximum or minimum value, and what that value is. Determine the domain and range. Give an equation for the axis of symmetry. y = x 2 - 4x + 4 Verify using the table and the graph function on your calculator.

y = ax 2 + bx + c y-intercept (o,c) vertex (-b/2a, ?) x-intercepts Let y = o and solve by factoring or using quadratic formula. Example y = 2x 2 – 12x + 16

y = a(x – h) 2 + k y-intercept (o,?) vertex (h,k) x-intercepts Let y = o and solve by working backwards. Example y = 2(x – 3) 2 - 2

y = a(x – p)(x – q) y-intercept (o,?) vertex ((p + q)/2, ?) x-intercepts p and q Example y = 2(x – 4)(x – 2)

Solve by factoring. a)2x 2 – 14x + 20 = 0 b)16x 2 – 9 = 0 c)5x 2 + 13x = 6 Answers a) x = 5 or x = 2 b) x = ± ¾ c) x = 2/5 or x = -3

Solve by using the quadratic formula. a) 3x 2 – 11x – 4 = 0 b) x 2 – 4x + 13 = 0 c) x 2 + 9 = 8x Answers:a)x = 4 or x = -1/3 b)x = 2 ± 3i c)x = 4 ± √7

Solve by completing the square. a) x 2 – 6x + 5 = 0 b) x 2 + 8x + 3 = 0 c) 2x 2 – 8x – 24 = 0 d) -3x 2 + 6x – 3 = 0 Answers:a) x = 5 or x = 1b)x = -4 ±√13 c) x = 6 or x = -2d)x = 1

Write an equation for the parabola with a vertex at (2,-1) which has a y-intercept of 4.

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