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Chapter 3: Problem 96

Find the axis of symmetry for each parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose \(y\) -coordinate is the same as the given point. $$f(x)=(x-3)^{2}+2 ; \quad(6,11)$$

Short Answer

Expert verified
The axis of symmetry of the parabola is \(x=3\), and a second point on the parabola with the same \(y\)-coordinate as the given point (6,11) is (0,11).

Step by step solution

01

Establish the Axis of Symmetry

The given equation is of the form \(f(x) = (x-h)^2 + k\). Here, \(h=3\). Therefore, the axis of symmetry is \(x=3\).
02

Find the Second Point

Point (6,11) lies on the parabola. Applying the property of symmetry, there exists another point on the parabola \((2h-a, b) = (2*3 - 6, 11) = (0,11)\). So, (0,11) is the second point on the parabola with the same \(y\)-coordinate as (6,11).

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