1. Section 10.2 “Graph y = ax² + bx + c”
Properties of the Graph of a Quadratic Function
y = ax² + bx + c is a parabola that:
-opens up if a > 0
-opens down if a < 0
-is narrower than y = x² if the |a| > 1
-is wider than y = x² if the |a| < 1
-has an axis of x = -(b/2a)
-has a vertex with an x-coordinate of -(b/2a)
-has a y-intercept of c. So the point (0,c) is on the parabola

2. Finding the Axis of Symmetry and the Vertex of a Parabola
Consider the graph y = -2x² + 12x – 7
(a) Find the axis of symmetry of the graph
(b) Find the vertex of the graph
Axis of symmetry:
Substitute
a = -2
b = 12
Substitute the x-value into the original equation and solve for y.
The vertex of the parabola
is the point (3,11)

3. Graph y = 3x² - 6x + 2 Step 1: Determine if parabola opens up or down
Step 2: Find and draw the
axis of symmetry
Step 3: Find and plot the vertex
Step 4: Plot two points. Choose two x-values less than the x-coordinate of the vertex. Then find the corresponding y-values. x y 2 -1 11
Step 5: Reflect the points plotted over the axis of symmetry.
Step 6: Draw a parabola through the plotted points.
Minimum Value

4. Graph y = -1/4x² - x + 1 Step 1: Determine if parabola
opens up or down
DOWN
Step 2: Find and draw the
axis of symmetry
Step 3: Find and plot the vertex
Step 4: Plot two points. Choose two x-values more than the x-coordinate of the vertex. Then find the corresponding y-values. x y 1 2 -2
Step 5: Reflect the points plotted over the axis of symmetry.
Maximum Value
Step 6: Draw a parabola through the plotted points.

5. Minimum and Maximum Values
For y = ax² + bx + c, the y-coordinate of the vertex is the MINIMUM VALUE of the function if a > 0 or the MAXIMUM VALUE of the function if a < 0.
y = ax² + bx + c; a > 0
y = -ax² + bx + c; a < 0
maximum
minimum