SOLUTION: Find the vertex, the line of symmetry, and the maximum or minimum value of the quadratic function,and graph the function. f(x)=4x^2-32x+66

Question 440659: Find the vertex, the line of symmetry, and the maximum or minimum value of the quadratic function,and graph the function.
f(x)=4x^2-32x+66
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

For any quadratic function of the form:

the

-coordinate of the vertex of the graph is found by:

and the

-coordinate of the vertex is found by:

The equation of the axis of symmetry is:

If the lead coefficient is positive, the parabola opens upward and the vertex is a minimum. If the lead coefficient is negative, the parabola opens downward and the vertex represents a minimum.

The

-coordinate of the vertex is the minimum (or maximum) value of the function.

To graph:

1. Calculate the coordinates of the vertex. Plot the vertex.

2. Plot the point (0, c)

3. Set the function equal to zero. Calculated the discriminant of the quadratic formula. If positive, there are two real roots. Use the quadratic formula to determine the roots and plot the points. If zero, the vertex is at the x-axis. If negative, there are no

intercepts.

4. Plot the point

which is a point on the parabola by symmetry.

5. If there were no

-intercepts in step 3, pick a value for

, and then evaluate the function. Do this as often as you like to plot extra points

6. Draw a smooth curve through the plotted points.

John

My calculator said it, I believe it, that settles it

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