Answer:
Vertex = (0,-1)
The x value of its largest x-intercept is [tex]x=\frac{1}{2}[/tex].
The y value of the y-intercept is y = -1.
Step-by-step explanation:
The given function is
[tex]f(x)=4x^2-1[/tex] .... (1)
The vertex form of a parabola is
[tex]g(x)=a(x-h)^2+k[/tex] ..... (2)
where, a is a constant, (h,k) is vertex of the parabola.
From (1) and (2) we get
[tex]a=4,h=0,k=-1[/tex]
So, the vertex of the parabola is (0,-1).
Substitute f(x)=0 in equation (1) to find x-intercepts.
[tex]0=4x^2-1[/tex]
Add 1 on both sides.
[tex]1=4x^2[/tex]
Divide both sides by 4.
[tex]\frac{1}{4}=x^2[/tex]
Taking square root both sides.
[tex]\pm \sqrt{\frac{1}{4}}=x[/tex]
[tex]\pm \frac{1}{2}=x[/tex]
The x-intercepts are [tex]-\frac{1}{2}[/tex] and [tex]\frac{1}{2}[/tex].
Therefore the x value of its largest x-intercept is [tex]x=\frac{1}{2}[/tex].
Substitute x=0 in equation (1) to find the y-intercept.
[tex]f(0)=4(0)^2-1=-1[/tex]
Therefore the y value of the y-intercept is y = -1.
