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Chapter 9: Q. 276 (page 945)

In the following exercises, find the maximum or minimum value of each function:

y=4x2鈭�49

Short Answer

Expert verified

The minimum value of the function is-49and it happens whenx=0.

Step by step solution

01

Step 1. Given Information

The given function isy=4x2-49.

We have to find the maximum or minimum value of the function.

02

Step 2. Finding the equation of the axis of symmetry

Step 2. Finding the equation of the axis of symmetry

Since the value of the leading coefficient is positive, the parabola opens upward.

Thus, the quadratic equation has a minimum.

Now,

x=-b2ax=-02(4)x=0

The equation of the axis of symmetry isx=0.

03

Step 3. Find f(0)

The vertex is on the linex=0

So, evaluate y(0)by substituting x=0in the given function.

y=4(0)2-49y=0-49y=-49

So, the vertex is(0,-49).

The minimum value of the quadratic is -49and it occurs whenx=0.

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