Question

Write the quadratic function in the form f(x) = a * (x - h) ^ 2 + kf(x) = - 2x ^ 2 + 4x - 3Then, give the vertex of its graph.

Answer 1

Given

`f(x)=-2x^2+4x-3`

Solution

`\begin{gathered} f(x)=-2x^2+4x-3 \\ f(x)=ax^2+bx+c \\ in\text{ vertex form} \\ f(x)=a(x-h)^2+k \\ \\ h=-(b)/(2a)=-(4)/(2(-2))=-(4)/(-4)=1 \\ \\ k=f(h)^ \\ k=-2(1)^2+4(1)-3 \\ k=-2+4-3 \\ k=2-3 \\ k=-1 \end{gathered}`

The quadratic in vertex form is

`f(x)=-2\left(x-1\right)²-1`

The vertex is

`Vertex\text{ }\lparen1,-1)`

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