Quadratic functions

1003162303

Level:

Find all the values of the real parameter

m

such that

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

is increasing on

(0; \infty)

m \in [0; \infty)

m \in (- \infty; 0)

m \in (- \infty; 0]

m \in (- \infty; 2]

1003162302

Level:

Find all the values of the real parameter

m

such that

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

is an even function.

m = 0

m = 3

m = - 3

m \in (- \infty; \infty)

1003162301

Level:

Find all the values of the real parameter

a

such that

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

is decreasing on

(0; \infty)

a \in (- \infty; 0)

a \in (0; \infty)

a \in [2; + \infty)

a \in (- \infty; 2]

1003108312

Level:

The graph of the function

f

is a parabola, vertex of which is

[6; 0]

and

f (2) = 8

is given. Find the function

f

f (x) = \frac{1}{2} (x - 6)^{2}

f (x) = - \frac{1}{2} (x - 6)^{2}

f (x) = \frac{1}{2} (x + 6)^{2}

f (x) = \frac{1}{2} x^{2} + 6

1003108311

Level:

The quadratic function

f

has the minimum at

x = - 2

and its graph passes through the points

[0; 13]

[- 1; 4]

. Find the function

f

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

f (x) = - \frac{5}{9} (x - 2)^{2} + 9

f (x) = \frac{5}{9} (x - 2)^{2} + 9

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

1003108310

Level:

The graph of the quadratic function

f

has the vertex at the point

[3; - 1]

and it passes through the point

[- 1; 3]

. Find the function

f

f (x) = \frac{1}{4} x^{2} - \frac{3}{2} x + \frac{5}{4}

f (x) = \frac{1}{4} x^{2} + \frac{3}{2} x + \frac{5}{4}

f (x) = - \frac{1}{4} x^{2} + \frac{3}{2} x - \frac{13}{4}

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

1003108309

Level:

The graph of the quadratic function

f

intersects coordinate axes at the points

[- 3; 0]

[1; 0]

[0; \frac{3}{2}]

. Find the function

f

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

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

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

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

1003108308

Level:

Which of the following information are insufficient to determine quadratic function uniquely?

two intersection points with the

x

-axis and

x

-coordinate of the vertex

two intersection points with the

x

-axis and

y

-coordinate of the vertex

two intersection points with the

x

-axis and any other point of the function

coordinates of the vertex and the intersection with the

y

-axis

1003108307

Level:

Choose the triple of points, such that the graph of any of the functions

f (x) = a x^{2} + c

, where

a \in R ∖ 0

c \in R

, does not pass through all three points.

[- 2; 5]

[2; 1]

[0; 3]

[- 2; 5]

[2; 5]

[0; 3]

[- 2; 5]

[2; 5]

[0; 7]

[- 2; 5]

[0; 0]

[1; 1]

1003108306

Level:

The

x

-axis is the tangent line of the graph of the quadratic function

f

. The point of tangency has the coordinates

[- 2; 0]

. Given

f (- 1) = - 4

, find the function

f

f (x) = - 4 x^{2} - 16 x - 16

f (x) = - 4 x^{2} - 16 x + 16

f (x) = - \frac{4}{9} x^{2} + \frac{16}{9} x - \frac{16}{9}

f (x) = 4 x^{2} - 16 x + 16

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