# How to graph a parabola y=4x^2?

May 19, 2018

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#### Explanation:

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Given the Equation : color(red)(y=f(x)=4x^2

A Quadratic Equation takes the form:

color(blue)(y=ax^2+bx+c

Graph of a quadratic function forms a Parabola.

The coefficient of the color(red)(x^2 term (a) makes the parabola wider or narrow.

If the coefficient of the color(red)(x^2, term (a) is negative. then the parabola opens down.

The term Vertex is used to identify the Turning Point of a parabola.

It can be maximum point or minimum point, depending on the sign of the coefficient of the color(red)(x^2 term.

color(green)("Step 1 :"

Create a data table as shown below: Notice that the column E contains values for color(red)(x^2

$y = {x}^{2}$ is the Parent Function for a quadratic equation.

The graph of $y = {x}^{2}$ is useful in understanding the behavior of the function given color(red)(y = 4x^2.

Since, the sign of the ${x}^{2}$ term is positive, the parabola opens up and we have a Minimum point at the Vertex.

color(green)("Step 2 :"

Plot the Points from the data table to draw graphs.

Graphs of color(red)(y=x^2, the parent function and color(blue)(y=4x^2 are: Observe that the coefficient of the color(red)(x^2, which is $4$, makes the parabola of $y = 4 {x}^{2} ,$ narrow.

Hope it helps.