5.1 Graphing Quadratic Functions

Algebra 2

Learning Check

• I can graph quadratic equations of the form y = (x – h)2 + k, and identify the vertex and the equation of the axis of symmetry of a parabola.

What do you have to do?

• I was going to go into a long explanation. However, the long and short of it—here’s what you have to do:– Axis of symmetry– Find the vertex– Choose 5 points to graph the parabola– Write the equation

Ex. 1: Name the vertex and axis of symmetry for the graph of each equation.

y = (x + 8)2 – 1 . How is this graph different from y = x2

Remember the format. y = (x – h)2 + k

The vertex is at (h, k), but h is opposite because the negative sign. So, if you look at the equation, the vertex should be at (-8, -1).

Ex. 1: Name the vertex and axis of symmetry for the graph of each equation.

y = (x + 8)2 – 1 . How is this graph different from y = x2

The axis of symmetry happens to be whatever the h is in (h, k). So in this case, h = - 8, so x = -8.

It differs from the graph y = x2

in that the vertex is translated 8 units to the left and 1 unit down.

Ex. 2: Name the vertex and axis of symmetry for the graph of each equation. Table of values

y = (x + 1)2 +3. Then draw the graph.

The vertex is (h, k)—opposite h. (-1, 3) The axis of symmetry will be x = -1.

x (x + 1)2 +3 y

-4 (-4 + 1)2 +3 12

-3 (-3 + 1)2 +3 7

-2 (-2 + 1)2 +3 4

-1 (-1 + 1)2 +3 3

0 (0 + 1)2 +3 4

1 (1 + 1)2 +3 7

2 (2 + 1)2 +3 12

Ex. 2: Name the vertex and axis of symmetry for the graph of each equation.

y = (x + 1)2 +3. Then draw the graph.

The vertex is (h, k)—opposite h. (-1, 3) The axis of symmetry will be x = -1.

10

8

6

4

2

5 10 15

+3

Notice that the points with the same y-coordinates are the same distance from the axis of symmetry, x = -1

Ex. 3: Write the equation of the quadratic function for each graph.

8

6

4

2

-2

-4

5 10

The vertex of this parabola is at (-2, 0) which is (h, k)

y = (x – h)2 + k,

y = (x – (-2))2 + 0

y = (x + 2)2 + 0

Ex. 4: Write each equation in the form y = (x – h)2 + k. Then name the vertex and the axis of symmetry.

19. f(x)= x2 – 4x +4 (You have to factor. If you can’t recognize this yet, you are in trouble.)

y = (x – 2)2 + 0

The vertex is at (2, 0) and the axis of symmetry is at x = 2

Ex. 5: Write each equation in the form y = (x – h)2 + k. Then name the vertex and the axis of symmetry.

22. f(x)= x2 – 7

y = (x – 0)2 – 7

The vertex is at (0, -7) and the axis of symmetry is at x = 0

Assignment

• pp. 363-364 #6-42 all

What do you have to do?

• Problems #27-42, you have to graph. You need the following: – Write the equation – Axis of symmetry– Find the vertex– Choose 5 points to graph the parabola– Graph the parabola