1) if you want to find the roots:
For this case we have the following quadratic equation:
[tex]y = 4x ^ 2-5[/tex]
To find the solutions we do [tex]y = 0:[/tex]
[tex]4x ^ 2-5 = 0[/tex]
We add 5 to both sides of the equation:
[tex]4x ^ 2 = 5[/tex]
DIviding between 4 to both sides of the equation:
[tex]x ^ 2 = \frac {5} {4}[/tex]
We apply square root to both sides:
[tex]x = \pm \sqrt {\frac {5} {4}}\\x = \pm \frac {\sqrt {5}} {2}[/tex]
Thus, the roots are:
[tex]x_ {1} = \frac {\sqrt {5}} {2}\\x_ {2} = - \frac {\sqrt {5}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {\sqrt {5}} {2}\\x_ {2} = - \frac {\sqrt {5}} {2}[/tex]
2): if you want to write the equation in vertex form:
The general quadratic equation is:
[tex]y = a(x-h)^2+k[/tex]
where,
a: is the leading coefficient
(h,k): is the verex of the quadratic equation
Comparing with the original equation we have
[tex]y = 4x ^ 2-5[/tex]
So, the vertex is:
[tex](h,k)=(0,-5)[/tex]
Answer
The quadratic equation in vertex form is:
[tex]y = 4x ^ 2-5[/tex]
