Graphs of Quadratic Functions

The parabola and its features.

12 problems · about 21 minutes · F-IF.C.7, F-IF.B.4

NameDate

Figure — use these to answer the problems

Make a negative and the parabola flips. Change b and watch the vertex slide sideways.

y = 1x² − 4x + 3

b-4

Figure 1

Straightforward practice. Get the method working first.

5 problems

y = x² − 8x + 1. What is the vertex x-coordinate?
Answer
2
What does a negative leading coefficient mean?
- The parabola opens downward and has a maximum.
- The parabola opens to the left.
y = x² − 6x + 5. Vertex x-coordinate?
Answer
y = 2x² + 8x. Vertex x-coordinate?
Answer
y = −x² + 4. Does it open up or down? 1 up, 2 down.
Answer

The same ideas with more to keep track of.

3 problems

y = 3x² − 12x + 7. What is the y-intercept?
Answer
y = x² − 6x + 5 at x = 3. What is y?
Answer
A parabola opening upward has a maximum or minimum? 1 maximum, 2 minimum.
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each coefficient by what it controls.
Write each item under the heading it belongs to: The sign of a · The size of a · The value of c · The value of b
Direction and width
Position on the grid
y = x² − 10x + 2. Vertex x-coordinate?
Answer
The Turning Point
y = x² − 4x + 3. What is the x-coordinate of the vertex?
Answer
The Intercept
y = x² − 4x + 3. What is the y-intercept?
Answer