Linear/Quadratic Systems
Solve by graphing. How many solutions does the following system have?
y = x² - 2x - 3
y = -5
No solution
p2 + -2p - 15 = 0
x = {5, -3}
4x2 + 25 = 125
x= 5 or x = -5
m2 − 5m − 14 = 0
{7, −2}
Dylan sketches a parabola with a vertex at the origin that opens downward. What is the equation of Dylan's function?
y = -x^2
Solve by graphing. How many solutions does the following system have?
y = -x² + 2x + 7
y = -2x + 2
2 solutions
n2 + 12n + 36 = 0
x = {-6)
(4x + 1)2 - 16 = 0
x = 3/4 or x = -5/4
b2 − 4b + 4 = 0
{2}
Describe the transformation.
y = 1/6(x-3)2 + 1
Vertically compressed, and translated 3 units to the right and 1 unit down.
Solve using substitution. State the solutions.
y = x² + 4x + 5
y = 2x + 3
(-4, -5) and (2, 7)
7r2 + 49r + 84 = 0
7(r^2 + 7r + 12) = 0
x = {-4, -3}
34 = (a - 2)2 - 2
a = 8 or a = -4
2x2 − 3x − 5 = 0
{5/2 , −1}
Michelle transforms the quadratic parent function by vertically stretching the parabola by a factor of 5. Then, she translates the parabola 9 units up and 4 units right. What is the equation of Michelle's parabola?
y = 5(x-4)2 +9
Solve using substitution. State the solutions.
y = x² - 6x + 5
2x + y = 5
(0,5) and (4, -3)
3v2 + 12v = 15
3(v^2 + 4v - 5) = 0
x = {-5, 1}
0 = 3(x + 7)2 - 24
x = -7 + 2 square root of 2
or
x = -7 - 2 square root of 2
9n2 = 4 + 7n
{ 7 + square root of 193 / 18, 7 - square root of 193 / 18}
Describe the transformation.
y = -1/2(x + 6)2 - 2
Vertically compressed by a factor of 1/2, reflected across the x-axis, translated left 6 units, and translated down 2 units.