Answer:
[tex]y=3x^2-6x-3[/tex]
Step-by-step explanation:
Use the quadratic equation in vertex form:
[tex]y=a(x-h)^2+k[/tex] where (h, k) are the coordinates of the vertex
Therefore, substituting h = 1 and k = -6 into the equation:
[tex]y=a(x-1)^2-6[/tex]
Now substituting the point (4, 21) to find [tex]a[/tex]:
[tex]y=a(4-1)^2-6=21[/tex]
[tex]9a=27[/tex]
[tex]a=3[/tex]
Therefore, the final equation is: [tex]y=3(x-1)^2-6[/tex]
Expanding out the brackets and collecting like terms, this can be written as: [tex]y=3x^2-6x-3[/tex]
