Answer:
[tex]y = {x}^{2} - 2[/tex]
Or if you want with the value of h too.
[tex]y = {(x - 0)}^{2} - 2[/tex]
Step-by-step explanation:
[tex]y = a {(x - h)}^{2} + k[/tex]
Find the value of h and k by using the formula.
[tex]h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} [/tex]
From y = x²-2
[tex]a = 1 \\ b = 0 \\ c = - 2[/tex]
Substitute these values in the formula.
[tex]h = - \frac{0}{2(1)} \\ h = 0[/tex]
Therefore, h = 0.
[tex]k = \frac{4(1)( - 2) - {0}^{2} }{4(1)} \\ k = \frac{ - 8}{4} \\ k = - 2[/tex]
Therefore, k = - 2.
From the vertex form, the vertex is at (h, k) = (0,-2). Substitute h = 0, a = 1 and k = -2 in the equation.
[tex]y = a {(x - h)}^{2} + k \\ y = 1 {(x - 0)}^{2} - 2 \\ y = {(x)}^{2} - 2 \\ y = {x}^{2} - 2[/tex]
These type of equation where b = 0 can also be both standard and vertex form.
