MATH 9 DIAGNOSTIC TEST

Which of the following represents a quadratic equation?

• $ax+b=c\ \ \ with\ a\ne0$

• $ax+b=0\ \ \ with\ a\ne0$

• $ax^2+bx+c=0\ \ \ with\ a\ne0$

• $ax^3+bx^2+c+d=0\ \ \ with\ a\ne0$

Which of the following quadratic equation describes by a=2, b=–9, and c=6?

• $6x^2+2x-9=0$

• $2x^2-9x+6=0$

• $6x^2-9x+2=0$

• $2x^2+6x-9=0$

The roots of a quadratic equation are 9 and -7. Which of the following quadratic equations has these roots?

• $x^2+2x-63=0$

• $x^2-2x+63=0$

• $x^2-2x-63=0$

• $-x^2+2x-63=0$

What is the nature of the roots of the quadratic equation if the value of its discriminant is -81?

• The roots are not real.

• The roots are irrational and not equal.

• The roots are rational and not equal.

• The roots are rational and equal.

The length of a rectangular garden is 7 m longer than its width and the area is 228 m². Which of the following is the measure of the length of the garden?

• 18 meters

• 19 meters

• 20 meters

• 21 meters

Which of the following is the solution set of x² + x -12 < 0?

• (-3,4)

• (-4,3)

• (-4,-3)

• (3,4)

The graph of y = x² - 4 is obtained by sliding the graph of y = x² ________________________.

• 4 units to the right

• 4 units to the left

• 4 units upwards

• 4 units downwards

Which of the following is the quadratic function illustrated by the graph?

• $y=x^2+4$

• $y=x^2-4$

• $y=\left(x+4\right)^2$

• $y=\left(x-4\right)^2$

If m is directly proportional to n, the equation must be written as __________.

• $m=kn$

• $k=mn$

• $m=\frac{k}{n}$

• $k=\frac{m}{n}$

If t varies inversely as w, then we can write the equation as_______.

• $t=kw$

• $k=tw$

• $w=\frac{k}{t}$

• $t=\frac{k}{w}$