Question

Algebraically determine each of the following for the function y=16 - 4x(squared). A) the x and y intercepts if any. B) the symmetry type (x axis, y axis, origin, or neither.)

Answer 1

A) x intercept: (2, 0) , (-2, 0)

y intercept: (0, 16)

B) symmetric about y axis

Explanation:

Given the function:

`y=16-4x^(2)`

To find:

Algebraically, A) find the x and y intercepts and B) the symmetry type.

Solution:

A) x intercept, let us put y = 0

`y=16-4x^(2)`

`0=16-4x^(2)\\\Rightarrow 4x^2=16\\\Rightarrow x^2=4\\\Rightarrow x =+2, -2`

x intercept: (2, 0) , (-2, 0)

For y intercept, put x = 0

`y=16-4x^(2)`

y = 16 - 0 =16

y intercept: (0, 16)

B) If the quadratic equation is given as:
`y=ax^2+bx+c`,

the axis of symmetry is a vertical line
`x=-(b)/(2a )`

Here, c = 16

b = 0 and

a = -4

So, Axis of symmetry is:

`x=-(0)/(2* (-4)) = 0`

which is the equation of y axis.

So, given equation is symmetric about y axis.