Factoring
x2 - 2x - 3 = 0
x = 3, x = -1
Solve the following quadratic equation using the method of your choice:
0 = x2 - 4
x = 2, x = -2
Solve:
x2 = 16
x = 4, x = -4
List the transformations
y = (x + 3)2 - 7
left 3, down 7
What are two other words that refer to the "solution" of a quadratic equation?
x-intercepts, zeroes, roots
3x2 + 2x - 5 = 0
x = 1, x = 5
Solve the following quadratic equation by factoring:
9x2 - 81x = 0
x = 0, x = 9
Solve:
4x2 + 3 = 84
x = 9/2, x = -9/2
List the transformations:
y = -(x + 2)2
reflect over x-axis, left 2
How many real solutions can a quadratic function have?
0, 1, or 2
x2 - 7x = - 6
x = 6, x = 1
Solve:
(k - 3)(5k + 1) = 0
k = 3, k = -1/5
Solve:
(x - 5)2 = 49
x = 12, x = -2
List the transformations:
y = -3(x - 4)2 + 1
reflect over x-axis, vert. stretch by 3, right 4, up 1
Name two ways to solve a quadratic equation.
Solving quadratics by taking square roots, by factoring, or by graphing
2x2 = 7x + 30
x = -5/2, x = 6
EXPLAIN why solving using square roots is a good choice for the following problem:
4x2 - 120 = 24
Only one term with a variable
Solve:
x2 + 9 = 0
No Real Solution
Draw a graph of a quadratic function that has NO solutions
{parabola should point AWAY from the x-axis}
What is the standard form of a quadratic equation?
ax2 + bx + c = 0
5n2 + 41n - 12 = -4 + 2n
n = 1/5, n = -8
Solve the quadratic:
-10x2 - 3x + 1 = 0
x = 1/5, x = -1/2
Solve:
2(x+7)2 - 5 = 13
x = -4, x = -10
Draw a graph of a quadratic function that has a single x-intercept at 3 and a y-intercept at -4
{concave down parabola with a vertex at (3,0) and going through (0, -4)}
What 2 pieces of information do you know about the graph of this function JUST BY LOOKING at the equation?
y = -4x2 + 5x + 8
*it will be concave down
*it has a y-intercept at 8