Quadratic Functions
Parent Function: y = x2
Domain: All real numbers
Range: All real numbers greater than, or equal to zero.
Standard Form: ax^2 + bx + c = 0
This is helpful for solving equations that you can't factor, or are just too difficult. It can also be used to find the vertex of the equation, with the equation -b/2(a) which will give you the value of X which is the plugged back into the equation to find the value of Y, giving you the vertex.
Vertex Form: f (x) = a(x - h)^2+ k
Writing the equation in Vertex Form lets you to graph the parabola of the function easier because you use it to find the vertex. To find the vertex, you use the equation -b/2(a), this will give you the value of X, you then plug this value into the equation to get the Y value. Just like you would when the equation is in standard form.
Types of Translations:
Horizontal:
A horizontal translation moves the graph to the left or the right.
Parent Function: y = x2
Domain: All real numbers
Range: All real numbers greater than, or equal to zero.
Standard Form: ax^2 + bx + c = 0
This is helpful for solving equations that you can't factor, or are just too difficult. It can also be used to find the vertex of the equation, with the equation -b/2(a) which will give you the value of X which is the plugged back into the equation to find the value of Y, giving you the vertex.
Vertex Form: f (x) = a(x - h)^2+ k
Writing the equation in Vertex Form lets you to graph the parabola of the function easier because you use it to find the vertex. To find the vertex, you use the equation -b/2(a), this will give you the value of X, you then plug this value into the equation to get the Y value. Just like you would when the equation is in standard form.
Types of Translations:
Horizontal:
A horizontal translation moves the graph to the left or the right.
Vertical: A vertical translation moves the graph up or down.
The uses of vertex form are to find the vertex of the quadratic equation, then the parabola can easily be graphed.
The uses of vertex form are to find the vertex of the quadratic equation, then the parabola can easily be graphed.
Dilations:
A dilation is when the parabola gets either bigger or smaller but it keeps the same relative shape.
A dilation is when the parabola gets either bigger or smaller but it keeps the same relative shape.
Reflections:
A reflection is when the parabola is reflected over either the X-axis or the Y-axis, creating a mirror image.
A reflection is when the parabola is reflected over either the X-axis or the Y-axis, creating a mirror image.
Axis of Symmetry:
The Axis of Symmetry is the line that runs down the center of the parabola, it is the X point of the vertex.
The Axis of Symmetry is the line that runs down the center of the parabola, it is the X point of the vertex.
Vertex:
The vertex is the point where the parabola crosses the X-axis.
The formula used to find the vertex is Y=a(x-h)^2+K.
Maximum/Minimum:
The maximum value is the Y-coordinate of a parabola that opens down. The Minimum value is the Y-coordinate of a parabola that opens up.
The vertex is the point where the parabola crosses the X-axis.
The formula used to find the vertex is Y=a(x-h)^2+K.
Maximum/Minimum:
The maximum value is the Y-coordinate of a parabola that opens down. The Minimum value is the Y-coordinate of a parabola that opens up.
Y-intercept:
This is the point where the graph crosses the Y-axis.
Roots:
The root of a quadratic function is the x-value, when the y-value is 0.
When the X-value is found, you plug it into the equation to find the other roots.
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The Quadratic Formula:
The quadratic formula is the formula used to solve quadratic equations. 1. The quadratic formula is used to find the roots of a quadratic equation. 2. The quadratic equation can be used to predict business profit and loss. 3. It can also be used to plot the course of moving objects. |