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# Quadratic Expressions and Equations Review (Grade 10)

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## Quadratic Expressions and Equations Review

1.
The lowest or highest point on a parabola is the                 .
1. vertex
2. slope
3. axis of symmetry
4. y-axis
2.
For $y=ax^2+bx+c$, if a > 0, then the parabola opens           , but if a < 0, then the parabola opens               .
3.
Which equation represents the parabola shown below?
1. $y = 1/2 x^2$
2. $y = -1/2 x^2$
3. $y=2x^2$
4. $y=-2x^2$
4.
How many real solutions does the equation $4x^2 + 4x +1 = 0$ have?
1. 0
2. 1
3. 2
4. more than 2
5.
What is the value of the discriminant of the equation $x^2 - 3x + 4 = 0?$ Then, use the value to determine whether the equation has two real solutions, one real solution, or no real solutions (two imaginary solutions).
1. 0; one real solution
2. -7; no real solution
3. 9; two real solutions
4. 8; two imaginary solutions
6.
What is the vertex of the following function?
$y=2(x-4)^2+3$
1. (4,3)
2. (4,-3)
3. (8,6)
4. (-4,3)
7.
Determine the vertex form of $y = x^2 + 8x + 10$.
1. $y = (x + 4)^2 + 10$
2. $y = (x + 4)^2 - 6$
3. $y = (x + 4)^2 + 26$
4. $y = (x - 4)^2 - 6$
8.
What is the the axis of symmetry of the quadratic equation $y=4x^2+6x-12 ?$
1. $x=-12$
2. $x=1/2$
3. $x=3/4$
4. $x=-3/4$
9.
What is the axis of symmetry of the following equation?
$y= (x-1)(x+5)$
1. x = -2
2. x = 1
3. x = -5
4. x = 2
10.
Factor the following expression:

$x^2 - x - 6$

11.
Factor.
$3x^2+13x-10$

12.
Factor. $9m^2 -16$
1. $(3m-4)(3m-2)$
2. $(3m-8)(3m+2)$
3. $(3m-4)(3m+4)$
4. $(3m-4)(3m-4)$
13.
Solve the quadratic equation: $x^2 - 4x + 4 = 0$

14.
Find the exact solutions to $x^2 - 3x + 1 = 0$ by using the Quadratic Formula.
1. $[-3+-sqrt(5)]/2$
2. $[3+-sqrt(13)]/2$
3. $[-3+-sqrt(13)]/2$
4. $[3+-sqrt(5)]/2$
15.
Solve the equation.

$21x^2-7x = 0$

16.
What is the y-intercept of the quadratic equation $y=3x^2+2x-5$ ?
1. (3,2)
2. (0,-5)
3. (0,5)
4. (-3,-2)
17.
What are the x-intercepts of the graph of $-x^2 +3x - 2 = 0 ?$
1. x = -1, x = -2
2. x = 1, x = 2
3. x = 1, x = -2
4. x = -1, x = 2
18.
Graph the following equation. Label the axis of symmetry, vertex, and roots (if applicable).
$y = 4x^2+4x-3$

19.
$4x^2+mx+1=0$ has equal roots. Hence the value(s) of m will be                   .
1. $2$
2. $-2$
3. $+-4$
4. $16$
20.
For the quadratic function $y = -2x^2-12x-10$:
a. Transform the equation to the form $y-k=a(x-h)^2$
b. Find the vertex
c. Find the x and y-intercepts
d. Sketch the graph

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