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Features of Quadratic Graphs

Last updated almost 4 years ago

11 questions

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Let’s continue to practice finding intervals of increase, decrease, positive, and negative when analyzing the characteristics of quadratic functions.  Look at the functions below.  Can you answer each characteristic with the correct intervals or ordered pairs?  You may use Desmos to help you.

Question 1

1.

Over what interval is f(x) increasing?

Question 2

2.

Over what interval is f(x) decreasing?

Question 3

3.

What are the x-intercepts of the function f(x)? (WRITE TWO ORDERED PAIRS)

Question 4

4.

When is f(x) positive?

Question 5

5.

When is f(x) negative?

x < -6

x > -2

-6 < x < -2

Question 6

6.

What is the vertex for the function f(x)?

Question 7

7.

Over what interval is f(x) increasing?

Question 8

8.

Over what interval is f(x) decreasing?

Question 9

9.

When is f(x) positive?

Always

Sometimes

Never

Question 10

10.

When is f(x) negative?

Always

Sometimes

Never

Question 11

11.

If you finished the first ten questions, try this

My function has a vertex that is (0, 0) and an axis of symmetry of x = 0.

My y-intercept is 5
and my vertex is (-2, 1).

The range of my function is y ≤ 1.

My function's y-intercept and vertex are the same.

For my function, f(x) is negative when
x < 0 and x > 2.

The zeros of my parabola are (-6, 0) and (-2, 0).

The x-intercepts of my parabola are opposites.

Find my function using the clue below:
f(-1) + f(4) = -11

My function is only increasing over the interval x > -1.

My minimum is y=1 and
all the y-values of my function are positive.

My function is decreasing over the interval (-4, ∞).

I have an axis of symmetry of x = -1.