Parts of a Quadratic
What is the y-intercept of a quadratic?
What does the letter d do to transform a quadratic?
Vertical shift (up/down)
Zero!
Solve: x2 - 16 = 0
x = -4, 4
Solve: x2 + 4x + 3 = 0
x = -3, -1
What is the vertex of a quadratic?
What does the letter a do to transform a quadratic?
Makes the curve thinner or wider
Factor and solve: x2 - 7x + 10 = 0
x = 2, 5
6x2 = 54
x = -3, 3
Solve: 2x2 + 5x + 4 = 0
Undefined / No Solutions
What is the x-intercept of a quadratic?
When the graph crosses/intercepts the x-axis
State the transformation of this quadratic:
y = x2 + 2
1. Shift up by 2
Factor and solve: x2 - 25 = 0
x = -5, 5
Solve: x2 + 25 = 0
UNDEFINED / NO SOLUTIONS
Solve: 2x2 - 8 = 0
x = -2, 2
What are the three other terms used for an x-intercept?
Solutions, Roots, and Zeros
State the transformations of this quadratic:
y = 3(x - 4)2
1. Thinner by 3
2. Shift right by 4
Factor and solve: 3x2 - 15x = 0
x = 0, 5
Solve: 3x2 - 108 = 0
x = -6, 6
Solve: x2 + 2x = 3 - 2x, round to the nearest tenth
x = -4.6, 0.6
What is the shape of a quadratic called?
Parabola
Name all the transformations of this quadratic:
y = -(x+3)2 - 5
1. Flip
2. Shift left by 3
3. Shift down by 5
Factor and solve: 2x2 - 10x + 3 = 3
x = 0, 5
Solve: 25x2 + 10 = 46
x = - 6/5, 6/5
Solve: -x2 + 7x + 18 = 0
x = -2, 9