SYSTEMS OF LINEAR EQUATIONS
Solve by graphing:
y = x + 2
y = −x + 4
(1, 3)
Evaluate:
(-2a^2b)^3
-8a^6b^3
Does the quadratic relation have max or min?
5x-2x²+4 = 0
max
The length of a rectangle is 4 meters longer than the width (x). Write a quadratic expression that represents the area (A) of the rectangle in terms of x.
A=x(x+4)
Find the midpoint of the points:
(−4, 2) and (6, −8)
(1, −3)
State the y-intercept of:
y = −2x² + 3x − 9
-9
State how many solutions the system has:
2x − 3y = 6
4x − 6y = 10
No solution
Solve using substitution:
y = 2x − 1
x + y = 5
(2, 3)
Expand and simplify:
(x + 4)(x − 7)
x² − 3x − 28
State the zeros of:
y = (−3x − 2)(2x + 1)
x = −2/3 and x=−1/2
Find the maximum value of:
y = −x² + 6x + 1
y=10
Find the distance between the points:
A(1, 3) and B(5, 3)
4
Solve:
2x² − 1 = 31
x=4 and x=-4
Find the equation of the line that passes through (−2, 5) and is perpendicular to:
3x + y = 7
y = (1/3)x + 17/3
Solve using elimination:
2x + 3y = 21
2x − y = 1
(3, 5)
Factor completely:
-6x² − 15x
-3x(2x+5)
Find the axis of symmetry of:
y = −x² − 6x + 4
x = −3
A garden has a length of x m and perimeter of 24 m. Write a quadratic expression for the area A in standard form.
A = -x^2+12x
The circle is centered at the origin with a radius of 4.
Does the point (−2, 3) lie inside, on, or outside the circle?
Inside the circle
An endpoint of a line segment is A(2, −4). The midpoint of the segment is M(6, 1).Determine the coordinates of the other endpoint.
(10, 6)
Factor fully:
12x² − 27
3(2x − 3)(2x + 3)
The equation of a line is 2x − 3y + 6 = 0.
Without rewriting it into slope-intercept form, find the equation of a line that is parallel to this line and passes through the point (4, −1).
2x − 3y − 11 = 0
State the number of real solutions:
4x² − 20x + 25 = 0
two equal real roots
State the vertex of:
y = −2x² + 8x − 6
(2,2)
A company’s revenue is modeled by:
R=−3x² + 36x − 20. What is the maximum revenue?
$88
A line passes through the point (2, −4) and has an x-intercept of 6. Determine the equation of the line.
y = x − 6
Solve the quadratic equation:
-12x^2+22x-8=0
x=4/3 and x=1/2
For the quadratic relation: y = x² + kx + 16
Find the value(s) of k so the parabola touches the x-axis exactly once.
k = ±8
A movie theatre sells adult tickets for $12 and student tickets for $8. In one night, 150 tickets were sold for a total of $1560. How many adult and student tickets were sold?
90 adults and 60 students
Solve the quadratic equation:
2x² − 7x − 4 = 0
x=4 and x=-1/2
Determine the equation of the parabola that has an axis of symmetry at x = 1 and passes through (0, 4) and (3, 1).
y = −(x − 1)² + 5
A triangle has a base of x metres and a height of 24−x metres. Find the maximum area of the triangle
72 m^2
Determine the equation of the perpendicular bisector of the segment joining the points (1, 2) and (7, −4).
y = x − 5
A ball is thrown upward from a height of 2 m and reaches a maximum height of 18 m after 2 seconds.
Write a quadratic equation in standard form that models the height of the ball.
h=−4t² + 16t + 2
Solve exactly:
(x − 1)(x + 5) = (x + 2)²
No solution