Parent function (Red) f(x)=x^{2}

A parabola that opens up and is wider than the parent function (blue) f(x)=1/2x^{2}+2

A parabola that opens down and is more narrow than the parent function. (purple) f(x) = -6x^{2}-1

A parabola that has been shifted to the right of the parent function. (orange) f(x) = (x-3)^{2}

A parabola that has been shifted down lower than the parent function. (green) f(x) =x^{2}-2

Significance of a, h, and k

Changing the values of a, h, and/or k can influence that parabola in different ways. Parabolas will open up when the a value is positive. And when the a value is negative it will open down as shown with the purple parabola. You can also make a parabola wider or more narrow by changing the A value. As shown with the blue and purple parabola with a smaller a your parabola is wider and with a larger number a value your parabola is more narrow. Essentially your a value determines the direction the parabola opens and the width of your parabola. For values h it determines if the parabola is shifted to the right or to the left. With the orange parabola you can see the that the value is negative 3. So it is shifted to the right three times. With the k value it determines if the parabola is shifted up or down. If the k value is positive the parabola is shifted up and if the k value is negative the parabola shifts down. The green graph has a k value of negative 2 so it is shifted down two spots. If you have the h and k value you can also determine the vertex. Which is the highest/lowest point in a parabola. Vertex would be (-h, k). If you have both of these value you are able to instantly put a point onto your graph which is beneficial to your parabola.

Self-Assessment

How did I represent the same mathematical idea in multiple ways in this assignment?

I showed my understanding of parabolas by being able to write out an equation and graph out the parabola and explain it well. Which shows multiple areas of understanding and different levels of explaining while following the problem that needs to be answered. Changing the equation to fit the criteria shows I am able to understand parabolas to the fullest extent of graphing and explaining everything that is required.

State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.

Vertex – The highest or lowest point on your parabola

Parabola – A shape of the graph reflecting a quadratic equation

A Value – Determines width and direction that it opens

K Value – A point that shifts up or down depending on if the k value if positive or negative

H Value – A point that shifts left or right depending on if the h value is positive or negative

Parent Function – The most basic parabola

How did you use formatting to share your information in a clear and organized way?

I made sure that everything is easy to read and understand by adding spaces between paragraphs and bolding the important questions that need to be answered. I also made sure to separate each major task with a heading to make everything more organized.