Consider the Quadratic function f(x) = 4x^2 - 1. Its vertex is Preview The x value of its largest x-intercept is x = The y value of the y-intercept is y = Preview Preview Preview

Answer:Its vertex is [tex](0,-1)[/tex].The x value of its largest x-intercept is [tex]\frac{1}{2}[/tex].The y value of the y-intercept is [tex]y = -1[/tex].Step-by-step explanation:A quadratic function in the format:[tex]f(x) = ax^{2} + bx + c[/tex]Has the vertex [tex](x_{v}, y_{v})[/tex] given by:[tex]x_{v} = -\frac{b}{2a}[/tex][tex]y_{v} = f(x_{v})[/tex]So[tex]f(x) = 4x^{2} - 1[/tex], we have that:[tex]a = 4, b = 0, c = -1[/tex]So[tex]x_{v} = -\frac{b}{2a} = -\frac{0}{8} = 0[/tex][tex]y_{v} = f(0) = 4*(0)^{2} - 1 = -1[/tex] Its vertex is [tex](0,-1)[/tex]The x-intercept values are the values of x when f(x) = 0;So[tex]f(x) = 0[/tex][tex]4x^{2} - 1 = 0[/tex][tex]4x^{2} = 1[/tex][tex]x^{2} = \frac{1}{4}[/tex][tex]x = \pm \sqrt{\frac{1}{4}}[/tex][tex]x = \pm \frac{1}{2}[/tex]The x value of its largest x-intercept is [tex]x = \frac{1}{2}[/tex].The y-intercept is the value of f(x) when x = 0, so,  f(0)[tex]f(x) = 4x^{2} - 1[/tex][tex]f(0) = 4*(0)^{2} - 1 = 0-1 = -1[/tex]The y value of the y-intercept is [tex]y = -1[/tex].