Quiz about Review Quadratics

Question 1

Expand and simplify $$\left(x+4\right)\left(2x-3\right)$$

Accepted Answer

$$2x^2+5x-12$$

Answer

$$2x^2-5x-12$$

Question 2

Expand and simplify $$\left(3x-4\right)\left(3x+4\right)$$

Accepted Answer

$$9x^2-16$$

Answer

$$9x^2+16$$

Question 3

Expand and simplify $$\left(2x+1\right)^2$$

Accepted Answer

$$4x^2+4x+1$$

Answer

$$4x^2+1$$

Question 4

Factorize $$x^2+5x-14$$

Accepted Answer

$$\left(x-2\right)\left(x+7\right)$$

Answer

$$\left(x-7\right)\left(x+2\right)$$

Question 5

Factorize $$2x^2-5x-3$$

Accepted Answer

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

Answer

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

Question 6

Solve $$x^2-8x+9=0$$

Accepted Answer

$$x=4\pm\sqrt[]{7}$$

Answer

$$x=2\pm\sqrt[]{7}$$

Question 7

Solve $$4x^2-6x-5=0$$

Accepted Answer

$$x=\frac{3}{4}\pm\frac{\sqrt[]{29}}{4}$$

Answer

$$x=\frac{3}{4}\pm\sqrt[]{29}$$

Question 8

The curve C has equation $$y=x^2-3x+2$$ . Find the coordinates of any points where C intersects the coordinate axes.

Accepted Answer

(1,0), (2,0), (0,2)

Answer

(1,0), (-2,0), (0,2)

Question 9

Write the quadratic function $$y=x^2+8x-9$$ in the form $$y=a\left(x+b\right)^2+c$$ , where a, b, and c are integers to be found.

Accepted Answer

$$\left(x+4\right)^2-25$$

Answer

$$\left(x+4\right)^2+7$$

Question 10

Write down the minimum point on the graph of $$y=x^2+8x-9$$

Accepted Answer

(-4,-25)

Answer

(-4,25)

Question 11

Find the coordinates of any points where $$y=x^2+8x-9$$ intersects the coordinate axes.

Accepted Answer

(-9, 0), (0, -9), (1, 0)

Answer

(0, -9), (1, 0), (9, 0)

Question 12

Find the coordinates of any points where $$y=2x^2+x-6$$ intersects the coordinate axes.

Accepted Answer

$$\left(-2,0\right),\left(0,-6\right),\left(\frac{3}{2},0\right)$$

Answer

$$\left(-2,0\right),\left(-\frac{3}{2},0\right),\left(0,-6\right)$$

Question 13

Find the coordinates of the turning point on the graph of $$y=2x^2+x-6$$

Accepted Answer

$$\left(-\frac{1}{4},-\frac{49}{8}\right)$$

Answer

$$\left(\frac{1}{4},-\frac{49}{8}\right)$$

Question 14

The function $$f\left(x\right)=kx^2+2kx-3$$ has two distinct real roots. Find the possible value of k

Accepted Answer

k<-3 or k>0

Answer

k>-3 or k<0

Question 15

The equation $$f\left(x\right)=2x^2-4x+3-2k$$ has real roots. Find the possible value of k

Accepted Answer

$$k\ge\frac{1}{2}$$

Answer

$$k>\frac{1}{2}$$

Question 16

The equation $$y=x^2+px+q$$ has no real roots. Find the possible value of $$p$$

Accepted Answer

$$p^2<4q$$

Answer

$$p^2>4q$$

Question 17

The graph below shows the curve $$f\left(x\right)=4-\frac{x^2}{8}$$ .

The curve is to be used as the model for the arc on a bridge where the water level under the bridge is represented by the x-axis. All measurements are in meters.

Write down the maximum height of the bridge above the water.

Accepted Answer

4 m

Answer

6 m

Question 18

Solve the equation $$x^4-13x^2+36=0$$

Accepted Answer

-3,-2,2,3

Answer

2,3

Question 19

Solve the simultaneous equations

$$3x^2+4y=83$$

$$3x+2y=-11$$

Accepted Answer

(-5,2), (7,-16)

Answer

(-2,5), (7,-16)

Question 20

Solve the simultaneous equations

$$x^2+10x+y^2=-20$$

$$y=2x+10$$

Accepted Answer

(-4,2), (-6,-2)

Answer

(-4,2), (-6,2)

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