2.2 Solving Quadratic Equations by Graphing

2.2 Solving Quadratic Equations by Graphing

Quadratic EquationQuadratic Function

y = 2x2 + 7x – 9f(x) = 2x2 + 7x – 9

Quadratic Form of a Function

F(x) = ax2 + bx + c

if a is (+) opens ______

if a is (-) opens ______

Identify the quadratic, linear, and constant term.

1) f(x) = 2x2 + 7x – 92) f(x) = x2 – 7

Parabola- a U shaped graph

opens ______opens ______

y value of vertex is minimumy value of vertex is maximum

D: {x/x is all reals} R: {y/ y ≥ k}D: {x/x is all reals} R: {y ≤ k}

There are 3 possible outcomes when solving a quadratic equation

1) 2)3)

2 real solutions1 real solutionno real solutions

(where x hits the x-axis)x =

x =

How many solutions does the graph have, what are they?

1)2)

Solve each function by graphing, find all parts of the graph

1) f(x) = x2 + 12x + 36

a) write in quadratic form

b) Find the vertex (use x = )

c) plug in x to find y

d) Vertex is:

Axis of symmetry is (x = ):

opens up or down?does it have a maximum or minimum value?

y-intercept is (c):

e) Graph, make a t-chart to find 4 more points)

f) how many solutions does it have an what is the domain and range.

2) Graph y = x2 – 9. Find the vertex, axis of symmetry, how it opens, does it have a minimum or maximum value, the y-intercept, the domain and range. Then graph

2.2 (day 2)

Do Now: Factor

1) x2 – 8x + 12 = 02) 3x2 + 12x

Ex 1: Find the zeros of each function (by factoring )

1) f(x) = x2 – 8x + 12 2) f(x) = 3x2 + 12x

Standard form of a parabola: y – k = a(x – h)2

Vertex: (h, k)Axis of symmetry: x = h

Ex 2:Name the vertex, axis of symmetry, how it opens. Then graph

a) y = - 2(x + 2)2- 3b) y – 1 = (x – 3)2

Ex 3:Write in standard form and graph

a) f(x) = x2 + 6x – 3

1) Rewrite using y

2) complete the square to put in standard form

3) Name the vertex, axis of symmetry y-intercept, how it opens, then graph

b) y = 2x2 + 8x + 16

1) complete the square

2) Name the vertex, axis of symmetry y-intercept, how it opens, then graph

Ex 4: Write an equation for each parabola

1)2)

a) plug in the vertex

b) plug into the equation another point

c) write the equation