Quiz about The Quadratic functions

Question 1

Which of the following functions is a quadratic function?

Accepted Answer

$$y=\left(2x-1\right)\left(x+3\right)$$

Answer

$$y=mx^2+3x-1$$ ( $$m$$ is a parameter)

Answer

$$y=2x+5$$

Answer

$$y=\sqrt[]{2x^2}-3x+1$$

Question 2

The function $$y=2x^2+4x-1$$ is

Accepted Answer

decreasing on the interval $$\left(-\infty;-1\right)$$ and increasing on the interval $$\left(-1;+\infty\right)$$

Answer

increasing on the interval $$\left(-\infty;-2\right)$$ and decreasing on the interval $$\left(-2;+\infty\right)$$

Answer

decreasing on the interval $$\left(-\infty;-2\right)$$ and increasing on the interval $$\left(-2;+\infty\right)$$

Answer

increasing on the interval $$\left(-\infty;-1\right)$$ and decreasing on the interval $$\left(-1;+\infty\right)$$

Question 3

The axis of symmetry of the parabola $$y=-2x^2+5x+3$$ has the equation:

Accepted Answer

$$x=\frac{5}{4}$$

Answer

$$x=-\frac{5}{4}$$

Answer

$$x=\frac{5}{2}$$

Answer

$$x=-\frac{5}{2}$$

Question 4

The vertex of the parabola $$y=3x^2-2x+1$$ is

Accepted Answer

$$I\left(\frac{1}{3};\frac{3}{2}\right)$$

Answer

$$I\left(\frac{1}{3};-\frac{3}{2}\right)$$

Answer

$$I\left(-\frac{1}{3};\frac{3}{2}\right)$$

Answer

$$I\left(-\frac{1}{3};-\frac{3}{2}\right)$$

Question 5

Given the quadratic function $$y=2x^2+bx+c$$ which has the vertex $$I\left(-1;3\right)$$ . Calculate $$b+c$$ .

Accepted Answer

$$9$$

Answer

$$-1$$

Answer

$$-9$$

Answer

$$1$$

Question 6

Find the maximum value of the function $$y=-\sqrt[]{2}x^2+4x$$ .

Accepted Answer

$$2\ \sqrt[]{2}$$

Answer

$$\sqrt[]{2}$$

Answer

$$2$$

Answer

$$4$$

Question 7

Which of the following functions reaches its minimum value at $$x=\frac{3}{4}$$ ?

Accepted Answer

$$y=x^2-\frac{3}{2}x+1$$

Answer

$$y=4x^2-3x+1$$

Answer

$$y=-2x^2+3x+1$$

Answer

$$y=-x^2+\frac{3}{2}x+1$$

Question 8

Which of the following four functions matches the graph shown in the figure?

Accepted Answer

$$y=-\frac{1}{2}x^2+x+\frac{3}{2}$$

Answer

$$y=-\frac{1}{2}x^2+x+\frac{5}{2}$$

Answer

$$y=x^2-2x$$

Answer

$$y=x^2-2x+\frac{3}{2}$$

Question 9

Given a quadratic function $$y=ax^2+bc+c$$ whose graph is shown in the figure. Which of the following statements is correct?

Accepted Answer

$$a>0,b<0,c>0$$

Answer

$$a>0,b<0,c<0$$

Answer

$$a<0,b<0,c>0$$

Answer

$$a>0,b>0,c>0$$

Question 10

Given the parabola $$y=ax^2+bx+c$$ .
Consider the signs of coefficient $$a$$ and the discriminant $$\Delta$$ ,
knowing that the graph intersects the x-axis at two distinct points and the vertex is below the x-axis.

Accepted Answer

$$a>0,\Delta>0$$

Answer

$$a<0,\Delta>0$$

Answer

$$a<0,\Delta<0$$

Answer

$$a>0,\Delta<0$$

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