Lesson 9.1 - 9.2 Graphing Quadratic Equations
1 root
How many roots / solutions does a quadratic equation have if the vertex is on the x-axis?
2 roots
How many roots / solutions does a quadratic equation that opens down with a vertex of (2, 4) have?
0 roots
How many roots / solutions does a quadratic equation that opens up with a vertex of (2, 4) have?
Maximum
If a quadratic equation opens downward, is the vertex a maximum or minimum?
Minimum
If a quadratic equation opens upward, is the vertex a maximum or minimum?
graph faces downwards
In the expression ax² + bx + c, what happens to the graph when the a value is negative?
a
In the expression ax² + bx + c, which value determines how the parabola opens?
x-value
Is the axis of symmetry the x-value of the vertex or the y-value of the vertex?
Minimum
Is the vertex for the quadratic equation x² - 4x + 6 = 0 a max or a min?
x = -b/(2a)
The formula for the axis of symmetry is
Axis of Symmetry
The line that splits a quadratic equation at the point of symmetry is called
False
True or false: Every parabola crosses the x-axis.
True
True or false: The domain for all quadratic functions is always "all real numbers."
True
True or false: The roots of a quadratic function are the x-intercepts.
False
True or false: Where the graph crosses the y-axis is called the root.
True
True or false: a quadratic function can have 0, 1, or 2 roots.
True
True or false: a quadratic function's graph is called a parabola.
True
True or false: the vertex is on the axis of symmetry.
0 roots
What are the roots of the graph shown?
x = {-3, -1}
What are the roots of the graph shown?
x = {-3, 1}
What are the roots of the graph shown?
x = 2
What is the axis of symmetry for the quadratic equation x² - 4x + 6 = 0?
x = 0
What is the axis of symmetry for the quadratic equation y = x² + 2?
x = -1
What is the axis of symmetry in the graph shown?
x = -2
What is the axis of symmetry in the graph shown?
x = 0
What is the axis of symmetry in the graph shown?
domain: all reals; range: y ≤ -4
What is the domain and range in the graph shown?
domain: all reals; range: y ≥ -1
What is the domain and range in the graph shown?
domain: all reals; range: y ≥ -4
What is the domain and range in the graph shown?
domain: all reals; range: y ≥ 1
What is the domain and range in the graph shown?
Vertex
What is the point at which the parabola begins to change direction?
(-1, -4)
What is the vertex in the graph shown?
(-2, -1)
What is the vertex in the graph shown?
(0, -4)
What is the vertex in the graph shown?
(0, 0)
What is the vertex in the graph shown?
Create an x / y table.
When graphing a quadratic equation, what is the step that follows finding the vertex?
Down
Will the graph for the quadratic equation f(x) = -2x² + 8x - 3 open up or down?