Quadractic Relationships

Prepared By: Dwight Williams

Graphing Vertex Form

Learning Checkpoint of Unit

  • I can use the mapping formula to graph vertex form equations
  • I can solve word problems using the vertex form

Using Finite Differences To Find a Quadratic Function

To find out if the graph is a non-linear the line would not be straight and going up by the same pace. If the line is straight that means it is a linear equation and will not be a quadratic function. as you can see in example one the graph is linear as it has a line of best fit. Not a curve of best fit.
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This graph is a non linear graph because it has a curve of best fit which means the line is curved and not straight. This means this graph has the potential of being a quadratic function.
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Quadratic functions/parabolas can be written in the form: y = a(x – h)2 + k

In a quadratic function/parabola there is a Vertex, the Optimal Value, and the Axis of Symmetry(AOS)

  • The vertex is the highest or lowest point of the graph (x,y)

  • The optimal value is the y value. The y value can tell you if the graph is going upward or downward. The y value is either the minimum value or maximum value. If it is the minimum value, then the graph is direction of opening is upward if it is maximum then the graph direction of opening is downward.

  • The axis of symmetry is the x value. It tells were the graph is reflected.

The "a" Value is the amount the parabola is strected or compressed. If the value of a is or greater than 1 the parabola will have a vertical stretch. as the parabola gets skinnier. If the number is below one, then it will be a compression as the parabola get wider. If the "a" value is negative, then the parabola will have a reflection in the x axis. If the a value is postive then the parabola will have a minimum value if the a value is negetive t hen the parabola will have a maximum value.
The Horizontal translation (h) is a translation moving left or right if the translation is to the left (negative), the h value becomes positive . When the translation is to the right (positive) the h value becomes negative. The h value helps us find the vertex so if you know your vertex you know your "x" value.
The vertical translation (k) is a translation going up or down. This value is the lowest or highest point in the graph. This value also helps us find the y value which will help us find the vertex.
Linear functions are written in the form: y = mx + b The first differences of a linear function are constant(the differences between y2 and y1are the same). But in a quadratic function, the second differences of a quadratic function are constant.

Step Pattern

To use graphing using step pattern there are a few key things one must do to do it properly. You need to know the Axis of symmetry also known as the x value. Then you need to know the optimal value also known as value. Which will give you your You also need to know the direction of opening. The direction of opening tells you if the graph is going down or up. you need to know the a value. Now to plot your points put your first point on the vertex as no other point can go past it. when you are graphing you will need 5 key points. To do mapping notation you need to multiply the a value by 1,3,5. if the a value was 2. You would multiply 2 by 1,3,5. Which would be That means starting from your vertex your first point would be over 1 up 2. Then start from the point you are currently on and go over 1 and up 6. Then from the you just made you would go over 1 and up 10. can do that on the opposite side of the vertex.
Graphing Quadratics Using Step Patterns

Graphing Formula

Graphing formula can be displayed in the form of mapping notation

x+h and ay+k

Mapping Notation

Finding X intercepts

  1. When finding the x-intercepts, plug 0 into y.
  2. Move k to the other side (don't forget to change the sign, positive or negative).
  3. Divide both sides with "a", completely canceling "a" on the side with the brackets. Leaving the brackets alone, "(x - h)^2".
  4. Square root both sides, completely canceling "^2" on the side with the brackets and getting rid of them, leaving you with "x - h".Solve by bringing over the number to leave the variable alone, and you have one of your x-intercepts.~ Solve again, but change the sign (positive/negative) of the number on the side with no variable and then solve, giving you your other x-intercept.

Word Problems

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