1. Warm Up Graph: 𝑦= 𝑥 2 +2𝑥−3 STEPS FOR GRAPHING y = ax2 + bx + c
Step 1: Find and plot the vertex.
The x –coordinate of the vertex is 𝒙= −𝒃 𝟐𝒂
Substitute this value for x in the equation and evaluate to find the
y -coordinate of the vertex.
Step 2: Draw the axis of symmetry. It is a vertical line through the vertex. Equation of axis of symmetry is x = # (x-coordinate of the vertex).
Step 3: Make an x-y chart. Choose 2 (or more) values for x to the right or left of the line of symmetry. Plug them in the equation and solve for y.
Step 4: Graph the points. Mirror the points on the other side of the line of symmetry. Draw a parabola through the points.

2. 5.2 Graphing Quadratic Functions in Vertex Form
11/13/13

3. Equations of a line…
Slope intercept form: y = mx + b Ex: y = 3x + 2 Point – slope form: y - y1 = m(x – x1) Ex: y – 5 = 3(x – 1) Standard form: Ax + By = C Ex: 3x – 2y = 5

4. Equations of a Parabola…
Standard Form: y = ax2 + bx + c Ex: y = 2x2 + 4x + 9 Vertex Form: y = a(x-h)2 + k

5. When a is positive, the parabola opens up.
Vertex Form:
a quadratic equation written in the form
Y = a(x –h)2 + k
(h, k) is the vertex
Again…
When a is positive, the parabola opens up.
When a is negative, the parabola opens down.
(h, k)
Graphing Method:
Step 1 Plot the vertex (h, k) from the equation
Steps 2-4 : same as the standard form.

6. Example 1
Graph ( )2 2 x – y = 1 +
The function is in vertex form where , h 2, and k Because a is negative, the parabola opens down. = a 2 – y k + ( )2 h x
STEP 1
vertex. ( )
h, k
2, 1 =
STEP 2
Draw the axis of symmetry through the vertex.
STEP 3
x y 1 -7 -1
When x = 0
𝑦=−2 0−
=−2 −
=−2(4)+1
=−8+1=−7
When x = 1
𝑦=−2 1−
=−2 −
=−2(1)+1
=−2+1=−1
STEP 4
Plot (0, -7) and (1, -1). Mirror them on the other side of axis of symmetry.
Draw a smooth curve through the points.

7. , h = 3, and k = -1. Because a is positive the parabola opens up. a =
Example 2 ( )2 3 x – y = 1
Graph
, h = 3, and k = -1. Because a is positive the parabola opens up. a = 1
STEP 1
vertex. ( )
h, k
3, -1 =
STEP 2
Draw the axis of symmetry through the vertex.
STEP 3
x y 4 5 3
When x = 4
𝑦= 4−3 2 −1
= (1) 2 −1 =0
When x = 5
𝑦= 5−3 2 −1
= (2) 2 −1
=4−1 =3
STEP 4
Plot (4, 0) and (5, 3). Mirror them on the other side of axis of symmetry.
Draw a smooth curve through the points.

8. , h = -1, and k = 4. Because a is positive the parabola opens up. a =
Example 3
Graph 4 y = ( )2 1 x 2 +
, h = -1, and k = 4. Because a is positive the parabola opens up. a = 2
STEP 1
vertex. ( )
h, k
-1, 4 =
STEP 2
Draw the axis of symmetry through the vertex.
STEP 3
x y 1 6 12
When x = 0 𝑦= =
=2(1)+4
=2+4=𝟔
When x = 1 𝑦= =
=2(4)+4
=8+4=𝟏𝟐
STEP 4
Plot (0, 6) and (1, 12). Mirror them on the other side of axis of symmetry.
Draw a smooth curve through the points.

9. Maximum and Minimum Value of the Quadratic Eqn.
Vertex is the highest point,
therefore the y-coordinate of the vertex is the maximum value.
Vertex is the lowest point,
therefore the y-coordinate of the vertex is the minimum value.

10. Take y-coordinate as the minimum value of the function.
Find the Minimum or Maximum Value
Tell whether the function has a minimum or maximum value. Then find the minimum or maximum value. ( )2 8 x y = 12 – 2 1 +
Find the vertex:
(h, k) is (-8, -12)
Since a is positive, the parabola opens up and the vertex is the lowest point.
Take y-coordinate as the minimum value of the function.
ANSWER
minimum; 12 –

11. 𝑦=− 𝑥 2 −2𝑥+1
Tell whether the function has a minimum or maximum value. Then find the minimum or maximum value.
𝑎=−1, b=−2, c=1
𝒙= −𝒃 𝟐𝒂
𝒙= −(−𝟐) 𝟐(−𝟏) = 𝟐 −𝟐 =−𝟏
𝑦= −1(−1) 2 −2 −1 +1=−1+2+1=2
Vertex (-1, 2)
Since a is negative, the parabola opens down and the vertex is the highest point.
Take y-coordinate as the maximum value of the function.
ANSWER
maximum; 2

12. Homework
WS 5.2