Quadratic Formula
Solve using the quadratic formula (round to the nearest tenth): 4x2 + 8x + 7 = 4
x = -0.5 and x = -1.5
Solving by completing the square (round to the nearest tenth): 3x2 + 12x + 81 = 15
No solution!
What is the formula for finding the vertex of a quadratic function?
Example: x2 + 4x + 10 = 0
Then put that value into the function to find the y-value.
Then you have your vertex (x, y)
Factor and find the zeros of the polynomial: x2 - 5x + 6 = 0
(x - 3)(x - 2) = 0
x = 3 and x = 2
Solve using the quadratic formula (round to the nearest tenth): x2 + 2x − 1 = 2
x = 1 and x = -3
Solving by completing the square (round to the nearest tenth): 2x2 - 2x + 7 = 5
No solution!
Identify the y-intercept, and tell if the function opens up or down.
-2x2 - 10x = 20
-2x2 - 10x - 20 = 0
y-intercept at y = -20
opens down!
Factor and find the zeros of the polynomial: x2 + 2x - 24 = 0
(x - 4)(x + 6) = 0
x = 4 and x = -6
Solve using the quadratic formula (round to the nearest tenth): 2x2 − 36 = x
x = 4.5 and x = -4
Solving by completing the square (round to the nearest tenth): 4x2 + 5 = 10x
x = 0.7 and x = 1.8
Identify the y-intercept, and tell if the function opens up or down.
x2 + 14x = -49
x2 + 14x + 49 = 0
y-intercept at y = 49
Opens up!
Factor and find the zeros of the polynomial: 3x2 + 11x - 20 = 0
(3x - 4)(x + 5) = 0
x = 4/3 and x = -5
Solve using the quadratic formula (round to the nearest tenth): 2x2 + 9x = −7
x = -1 and x = -3.5
Solving by completing the square (round to the nearest tenth): -2x2 + 10x = -14
x = -1.1 and x = 6.1
Graph the function and identify the zeros, axis of symmetry, and the vertex.
x2 + 2x - 24 = 0
(x + 6)(x - 4) = 0
zeros at x = -6 and x = 4
axis of symmetry at x = -1
vertex at (-1, -25)
Factor and find the zeros of the polynomial: 2x2 - 5x + 3 = 0
(2x - 3)(x - 1) = 0
x = 1.5 and x = 1
Create a polynomial that only has zeros at x = 5 and at x = -4.
x2 - x - 20, or any multiple of this
Solving by completing the square (round to the nearest tenth): -3x2 - 12 = 14x
x = -3.5 and x = -1.1
Graph the function and identify the zeros, axis of symmetry, and the vertex.
x2 - 10x + 16 = 0
(x - 8)(x - 2) = 0
zeros at x = 8 and x = 2
axis of symmetry at x = 5
vertex at (5, -9)
Factor and find the zeros of the polynomial: x2 - 12x + 36 = 0
(x - 6)2 = 0
x = 6