Quadratic functions

1003206001

Level:

We are given three quadratic functions:

\begin{aligned} f_{1} (x) & = - x^{2} - 2, \\ f_{2} (x) & = - x^{2} - 2 x - 4, \\ f_{3} (x) & = x^{2} + 2. \end{aligned}

Which of the given functions are increasing on the interval

(- 2; 0)

only

f_{1}

only

f_{2}

f_{1}

and

f_{2}

all three given functions

1003206201

Level:

Given

f (x) = 2 x^{2} - 6 x + 8

, find all input value(s) of

f

such that the output value of

f

5.5

x_{1} = \frac{5}{2}

x_{2} = \frac{1}{2}

x = 35.5

x_{1} = 13

x_{2} = 11

x_{1} = - \frac{5}{2}

x_{2} = - \frac{1}{2}

1003206202

Level:

Given

f (x) = - \frac{1}{2} x^{2} + x + \frac{3}{2}

, find all input values of

f

such that the output values of

f

are positive.

x \in (- 1; 3)

x \in (- \infty; - 1) \cup (3; + \infty)

x \in (- 3; 1)

x \in (- \infty; - 3) \cup (1; + \infty)

1103083101

Level:

The quadratic function

f

is graphed in the picture. Which of the following is its equation?

f (x) = - (x - 1)^{2} + 2

f (x) = (x - 1)^{2} + 2

f (x) = (x + 1)^{2} + 2

f (x) = - (x + 1)^{2} + 2

1103083102

Level:

The quadratic function

f

is graphed in the picture. Which of the following is its equation?

f (x) = \frac{1}{3} (x - 3)^{2} + 1

f (x) = 4 \cdot (x - 3)^{2} + 1

f (x) = (x + 3)^{2} + 4

f (x) = 4 \cdot (x + 1)^{2} + 3

1103083103

Level:

The quadratic function

f

is graphed in the picture. Which of the following is its equation?

f (x) = - x^{2} - 2 x + 1

f (x) = x^{2} + 2 x + 1

f (x) = - x^{2} + 2 x + 1

f (x) = - x^{2} - 4 x - 5

1103083104

Level:

The quadratic function

f

is graphed in the picture. Which of the following is its equation?

f (x) = \frac{2}{3} x^{2} - 4 x + 4

f (x) = x^{2} - 6 x + 7

f (x) = \frac{1}{3} x^{2} - 2 x + 1

f (x) = x^{2} - 2 x + 4

1103083105

Level:

The quadratic function

f

is graphed in the picture. Which of the following is its equation?

f (x) = - 2 x^{2} - 4 x - 5

f (x) = - 2 x^{2} + 12 x - 19

f (x) = - x^{2} - 2 x - 4

f (x) = x^{2} - 2 x - 5

1103083106

Level:

The quadratic function

f

is graphed in the picture. Which of the following is its equation?

f (x) = x^{2} + 6 x + 9

f (x) = x^{2} - 6 x + 9

f (x) = x^{2} - 3

f (x) = x^{2} + 3

1103083111

Level:

Find the graph of the quadratic function

f (x) = 2 x^{2} + 12 x + 16

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