QUADRATIC FUNCTIONSGraphing and Solving

GRAPHING QUADRATIC FUNCTIONS

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) = 2x2 + 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 = x2 - 4x + 4

Verify using the table and the graph function on your calculator.

STANDARD FORM

y = ax2 + bx + cy-intercept(o,c)vertex(-b/2a, ?)x-interceptsLet y = o and solve by factoring or using quadratic

formula.

Example y = 2x2 – 12x + 16

VERTEX FORM

y = a(x – h)2 + ky-intercept(o,?)vertex(h,k)x-interceptsLet y = o and solve by working backwards.

Example y = 2(x – 3)2 - 2

INTERCEPT FORM

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

Example y = 2(x – 4)(x – 2)

SOLVING QUADRATIC EQUATIONS

Solve by factoring.a) 2x2 – 14x + 20 = 0

b) 16x2 – 9 = 0

c) 5x2 + 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) 3x2 – 11x – 4 = 0

b) x2 – 4x + 13 = 0

c) x2 + 9 = 8x

Answers: a) x = 4 or x = -1/3b) x = 2 ± 3i c) x = 4 ± √7

Solve by completing the square.a) x2 – 6x + 5 = 0b) x2 + 8x + 3 = 0c) 2x2 – 8x – 24 = 0d) -3x2 + 6x – 3 = 0

Answers: a) x = 5 or x = 1 b) x = -4±√13

c) x = 6 or x = -2 d) x = 1

EXTRA CREDIT

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