Question

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

Answer 1

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Please read the explanation.

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=4x^2,` narrow.

Hope it helps.