How to graph a parabola $y = 4 x^{2}$ $y=4x^2$ ?

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Answer 1 · 2018-05-19T08:32:00

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**Given the Equation : ** $y = f (x) = 4 x^{2}$ $color(red)(y=f(x)=4x^2$

A Quadratic Equation takes the form:

$y = a x^{2} + b x + c$ $color(blue)(y=ax^2+bx+c$

Graph of a quadratic function forms a Parabola.

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

If the coefficient of the $x^{2},$ $color(red)(x^2,$ 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 $x^{2}$ $color(red)(x^2$ term.

$Step 1 :$ $color(green)("Step 1 :"$

Create a data table as shown below:

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Notice that the column E contains values for $x^{2}$ $color(red)(x^2$

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

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

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

$Step 2 :$ $color(green)("Step 2 :"$

Plot the Points from the data table to draw graphs.

Graphs of $y = x^{2}$ $color(red)(y=x^2$ , the parent function and $y = 4 x^{2}$ $color(blue)(y=4x^2$ are:

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Observe that the coefficient of the ** $x^{2}$ $color(red)(x^2$ , which is $4$ $4$ , makes the parabola of $y = 4 x^{2},$ $y=4x^2,$ narrow**.

Hope it helps.

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