Question

Write a quadratic formula vertex ( 2,3 ) point ( 1,-7 )

Answer 1

The vertex formula:

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

(h, k) - vertex

We have vertex (2, 3). Therefore:

$f(x)=a(x-2)^2+3$

We know that the parabola passes (1, -7).

Put the coordinates of this point into the function equation

x = 1, f(x) = -7

$a(1-2)^2+3=-7\ \ \ \ |-3\\\\a(-1)^2=-10\to a=-10$

Therefore we have:

$f(x)=-10(x-2)^2+3$

Use $(a-b)^2=a^2-2ab+b^2$

$f(x)=-10(x^2-2x(2)+2^2)+3=-10(x^2-4x+4)+3\\\\=-10x^2+40x-40+3=-10x^2+40x-37$

Answer: f(x) = -10x² + 40x - 37