Solve
Solve (x - 7)(x + 2) = 0
x = 7, x = -2
When solving quadratic equations, we are trying to find what feature of the parabola?
x-intercepts
This is the point where a quadratic function crosses the y-axis
y-intercept
Identify a, b and c in the following equation:
3x2 + 4x + 1 = 0
a = 3; b = 4; c = 1
Is this a quadratic equation?
x2 + 6x + 9 = 0
Yes because it is the quadratic form y = ax2 + bx + c where a does not equal zero.
Solve the following quadratic equation.
9x2 - 25 = 0
x = 5/3, x = -5/3
How many solutions can you have when solving a quadratic equation?
No solution, One solution or Two solutions
This point is the center of a parabola and can be a maximum or minimum, depending on the direction of the parabola.
Vertex
Identify a, b and c in the following equation:
x2 + 6x + 5 = 0
a = 1; b = 6; c = 5
Is this a quadratic equation? Explain your answer.
y = 9x3 + x2 - x + 8
No because the first x is cubed.
Solve the following quadratic equation.
x2 - 6x + 5 = 0
x = 5 x = 1
How do we know a quadratic function does not have solutions when looking at a graph?
It does not touch the x-axis
This line crosses the vertex of a parabola and divides the parabola in half.
Axis of Symmetry
Identify a, b and c in the following equation:
x2 - 9x + 20 = 9
a = 1; b = -9; c = 11
Solve the following
x2 - 5x - 24 = 0
x = 8, x = -3
Solve the following quadratic equation by completing the square.
x2 - 6x - 27 = 0
x = 9 x = -3
Why is the quadratic formula useful for solving quadratic equations?
We can ALWAYS use the quadratic formula, but we cannot always factor or simply take square roots.
What does a quadratic equation need to look like in order to solve by "taking square roots"?
(no linear term)
Solve the following quadratic equation: 2x2 + 9x + 4 = 0
x = -1/2 x = -4
Solve the following. Write your answer as a decimal.
2x2 +39 = -18x
x = -3.63397
x = -5.36603
Solve the following quadratic equation. State what method you used to solve.
2x2 - 5x - 3 = 0
x = -1/2 x = 3
How do we know a quadratic function does not have solutions when using the quadratic formula?
There will be a negative number under the square root.
When solving quadratic equations, what is another name for x-intercepts?
Solutions, Roots, Zeros
Solve the following quadratic equation: 4x2 - 17x - 15 = 0
State what method you used to solve it.
x = 5 x = -3/4
Solve
x2 = 2x + 48
x = 8 x = -6