Answer:
A) x intercept: (2, 0) , (-2, 0)
y intercept: (0, 16)
B) symmetric about y axis
Step-by-step explanation:
Given the function:
[tex]y=16-4x^{2}[/tex]
To find:
Algebraically, A) find the x and y intercepts and B) the symmetry type.
Solution:
A) x intercept, let us put y = 0
[tex]y=16-4x^{2}[/tex]
[tex]0=16-4x^{2}\\\Rightarrow 4x^2=16\\\Rightarrow x^2=4\\\Rightarrow x =+2, -2[/tex]
x intercept: (2, 0) , (-2, 0)
For y intercept, put x = 0
[tex]y=16-4x^{2}[/tex]
y = 16 - 0 =16
y intercept: (0, 16)
B) If the quadratic equation is given as: [tex]y=ax^2+bx+c[/tex],
the axis of symmetry is a vertical line [tex]x=-\frac{b}{2a }[/tex]
Here, c = 16
b = 0 and
a = -4
So, Axis of symmetry is:
[tex]x=-\dfrac{0}{2\times (-4)} = 0[/tex]
which is the equation of y axis.
So, given equation is symmetric about y axis.
