How do you graph the function #y=5xx^2#?
graph{5xx^2 [14.24, 14.23, 7.12, 7.12]}
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To graph the function ( y = 5x  x^2 ), follow these steps:

Identify the key components of the function: the coefficient of the linear term (5), and the coefficient of the quadratic term (1).

Determine the vertex of the parabola using the formula for the vertex of a quadratic function: ( \left( \frac{b}{2a}, f\left(\frac{b}{2a}\right) \right) ), where ( a = 1 ) and ( b = 5 ).

Calculate the ( y )intercept by setting ( x = 0 ) and solving for ( y ).

Find the ( x )intercepts by setting ( y = 0 ) and solving the resulting quadratic equation.

Plot the vertex, ( y )intercept, and ( x )intercepts on the coordinate plane.

Since the coefficient of ( x^2 ) is negative, the parabola opens downward.

Draw the parabola passing through the plotted points, with its vertex as the highest or lowest point depending on the sign of the coefficient of ( x^2 ).

Label the axes and any important points on the graph for clarity.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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