Question

The vertex of the graph of a quadratic function is (2.-1) and they intercept is (0,7). Which of the following is the equation of the function?

Answer 1

`\text{The vertex formula:}\\\\f(x)=a(x-h)^2+k\\\\(h;\ k)-\text{the coordinates of the vertex}`

`\text{We have:}\\\\\text{the vertex}\ (2;\ -1)\to h=2;\ k=-1\\\\\text{y-intercept}\ (0;\ 7)\to f(0)=7`

`\text{substitute:}\\\\f(x)=a(x-2)^2-1\\\f(0)=7\to a(0-2)^2-1=7\ \ \ |+1\\\\4a=8\ \ \ |:4\\\\a=2`

`\text{Answer in the vertex form:}\\\\f(x)=2(x-2)^2-1\\\\\text{Answer in the standard form:}\\\\f(x)=2x^2-8x+7`