Question

Write quadratic equation in standard form vertex (1,-6) passes through the point (4,21)

Answer 1

`y=3x^2-6x-3`

Explanation:

Use the quadratic equation in vertex form:

`y=a(x-h)^2+k` where (h, k) are the coordinates of the vertex

Therefore, substituting h = 1 and k = -6 into the equation:

`y=a(x-1)^2-6`

Now substituting the point (4, 21) to find
`a`:

`y=a(4-1)^2-6=21`

`9a=27`

`a=3`

Therefore, the final equation is:
`y=3(x-1)^2-6`

Expanding out the brackets and collecting like terms, this can be written as:
`y=3x^2-6x-3`