Pick up and do the Bellwork Quiz 9-2. (1-6) Only

To be able to SKETCH the graph of a quadratic equation. Today’s Objective To be able to SKETCH the graph of a quadratic equation. Take Notes when you see this icon….

y = ax2 +bx + c Quadratic Functions Quadratic functions are equations of the form ….. y = ax2 +bx + c Where a, b, and c are real numbers and a is not zero.

y = ax2 +bx + c Quadratic Functions And Finally the whole # Then comes the x term And Finally the whole # x2 term is always first

Find the values for a, b, and c in the following: 1.) y = 2x2 -5x + 12 a = 2, b= -5, c = 12 2.) y = 6 - x2 + 3x 2.) y = - x2 + 3x + 6 a = -1, b= 3, c = 6

Quadratic Functions The graph of a quadratic function is U shaped and is called a parabola. The end of the parabola is called the Vertex.

Quadratic Functions The line the U is wrapped around is called the Axis of Symmetry.

Consider the graph of y = x2 Parabola Y X Axis of Symmetry Vertex (0,0)

Quadratic Equations of the form: y = ax2 +bx + c 1.) If a is positive, the U is up. 2.) If a is negative, the U is down. 3.) The Vertex has an x-coordinate of -b/2a.

Now Lets Graph y = x2 - 2x - 3 1.) Make a T-Table. 2.) Pick 5 x values that are small, some negative, and don’t forget 0.

Now we will plug them into the equation y = x2 - 2x - 3 Now we will plug them into the equation x y -3 -1 1 3

y = x2 - 2x - 3 y = (-3)2 - 2(-3) - 3 y = 9 + 6 - 3 y = 12 12

y = x2 - 2x - 3 y = (-1)2 - 2(-1) - 3 y = 1 + 2 - 3 y = 0 12

y = x2 - 2x - 3 y = (0)2 - 2(0) - 3 y = - 3 12 -3

y = x2 - 2x - 3 y = (1)2 - 2(1) - 3 y = 1 - 2 - 3 y = -4 12 -3 -4

y = x2 - 2x - 3 y = (3)2 - 2(3) - 3 y = 9 - 6 - 3 y = 0 12 -3 -4

y = x2 - 2x - 3 Y X Vertex (1,-4)

y = x2 - 2x - 3 Use -b/2a to find the x coordinate of the vertex. -(-2)/2(1) = 2/2 = 1 The axis of symmetry is the line x = -b/2a, So…. X = 1 is the axis of symmetry.

y = x2 - 2x - 3 Y X Vertex (1,-4) Axis of Symmetry

You Try it, graph y = x2 - 2x - 5 1.) Make a T-Table. 2.) Pick 5 x values that are small, some negative, and don’t forget 0.

Now we will plug them into the equation y = x2 - 2x - 5 Now we will plug them into the equation x y -3 -1 1 3

y = x2 - 2x - 5 y = (-3)2 - 2(-3) - 5 y = 9 + 6 - 5 y = 10 10

y = x2 - 2x - 5 y = (-1)2 - 2(-1) - 5 y = 1 + 2 - 5 y = -2 10 -2

y = x2 - 2x - 5 y = (0)2 - 2(0) - 5 y = - 5 10 -2 -5

y = x2 - 2x - 5 y = (1)2 - 2(1) - 5 y = 1 - 2 - 5 y = -6 10 -2 -5 -6

y = x2 - 2x - 5 y = (3)2 - 2(3) - 5 y = 9 - 6 - 5 y = -2 10 -2 -5 -6

y = x2 - 2x - 5 Y X Vertex (1,-6)

y = x2 - 2x - 5 Now find the x coordinate using -b/2a - (-2)/2(1) = 2/2 = 1

Bellwork, Graph y = x2 + 4x + 3 1.) Make a T-Table. 2.) Pick 5 x values that are small, some negative, and don’t forget 0.

Now we will plug them into the equation y = x2 + 4x + 3 Now we will plug them into the equation x y -3 -1 1 3

y = x2 + 4x + 3 x y -3 -1 3 8 1 24 3

y = x2 + 4x + 3 Y X

Today’s Objective To be able to SKETCH the graph of a quadratic equation and find the Vertex.

y = ax2 +bx + c Quadratic Functions Quadratic functions are equations of the form ….. y = ax2 +bx + c Where a, b, and c are real numbers and a is not zero.

y = ax2 +bx + c Quadratic Functions And Finally the whole # Then comes the x term And Finally the whole # x2 term is always first

y = the equation with the x value plugged in Finding the Vertex x = -b/2a y = the equation with the x value plugged in

Find the x coordinate using -b/2a, then find the y coordinate. 1.) y = x2 + 4x + 3 2.) y = x2 + 3x - 7

y = 4 - 8 + 3 y = -1 Vertex = (-2,-1) x = - (4)/2(1) = -2 1.) y = x2 + 4x + 3 x = - (4)/2(1) = -2 y = x2 + 4x + 3 y = (-2)2 + 4(-2) + 3 y = 4 - 8 + 3 y = -1 Vertex = (-2,-1)

2.) y = x2 + 3x - 7 y = 9/4 - 9/2 - 7 y = -9 1/4 (-3/2,-9 1/4)

Find the x coordinate using -b/2a, then find the y coordinate. 1.) y = x2 + 2x - 8 2.) y = x2 - 3x - 4

y = 1 - 2 - 8 y = -9 Vertex = (-1,-9) 1.) y = x2 + 2x - 8

2.) y = x2 - 3x - 4 y = 9/4 - 9/2 - 4 y = -6 1/4 (3/2,-6 1/4)

Do the quadratic graphing worksheet Classwork Do the quadratic graphing worksheet

Try these graphs 1.) y = x2 - 3x - 4 2.) y = x2 + 3x - 7

1.) y = x2 - 3x - 4 Y X

1.) y = x2 - 3x - 4 y = 9/4 - 9/2 - 4 y = 4 (3/2,-6 1/4) - (-3)/2(1) = 3/2 1.) y = x2 - 3x - 4 1.) y = (3/2)2 - 3(3/2) - 4 y = 9/4 - 9/2 - 4 y = 4 (3/2,-6 1/4)

2.) y = x2 + 3x - 7 y = 9/4 - 9/2 - 7 y = 4 (-3/2,-9 1/4) - (3)/2(1) = -3/2 1.) y = x2 + 3x - 7 1.) y = (-3/2)2 + 3(-3/2) - 7 y = 9/4 - 9/2 - 7 y = 4 (-3/2,-9 1/4)

Rewrite each equation in standard form ….. 1.) 9 = 2x2 -5x + 12 0 = 2x2 -5x + 3 2.) 3 = 6 - x2 + 3x 0 = - x2 + 3x + 3