Question

Find the quadratic equation for y=4x^2-5

Answer 1

Answer:

y=4/x^3

Step-by-step explanation:

Answer 2

1) if you want to find the roots:

For this case we have the following quadratic equation:

$y = 4x ^ 2-5$

To find the solutions we do $y = 0:$

$4x ^ 2-5 = 0$

We add 5 to both sides of the equation:

$4x ^ 2 = 5$

DIviding between 4 to both sides of the equation:

$x ^ 2 = \frac {5} {4}$

We apply square root to both sides:

$x = \pm \sqrt {\frac {5} {4}}\\x = \pm \frac {\sqrt {5}} {2}$

Thus, the roots are:

$x_ {1} = \frac {\sqrt {5}} {2}\\x_ {2} = - \frac {\sqrt {5}} {2}$

Answer:

$x_ {1} = \frac {\sqrt {5}} {2}\\x_ {2} = - \frac {\sqrt {5}} {2}$

2): if you want to write the equation in vertex form:

The general quadratic equation is:

$y = a(x-h)^2+k$

where,

a: is the leading coefficient

(h,k): is the verex of the quadratic equation

Comparing with the original equation we have

$y = 4x ^ 2-5$

So, the vertex is:

$(h,k)=(0,-5)$

Answer

The quadratic equation in vertex form is:

$y = 4x ^ 2-5$