Which must be true of a quadratic function whose vertex is the same as the y-intercept ?

1 answer:

jeka943 years ago

3 0

A quadratic function whose vertex is the same as the y-intercept has the equation
y=x^2+k (where k is the y-intercept, with vertex (0,k))

Since the vertex coincides with the y-intercept, the axis of symmetry is x=0.

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A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis. What is the volume of the figure?

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Given:

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.

To find:

The volume of the figure.

Solution:

Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.

Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.

If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.

Volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$