which statement is true concerning the vertex and the axis of symmetry of $g(x)=5x^{2}-10x$?\nthe function…

which statement is true concerning the vertex and the axis of symmetry of $g(x)=5x^{2}-10x$?\nthe function written in vertex form is $g(x)=5(x - 1)^{2}-5$. the vertex is at $(1,-5)$ and the axis of symmetry is $x = 1$.\nthe vertex is at $(1,-5)$ and the axis of symmetry is $y = 1$.\nthe vertex is at $(0,0)$ and the axis of symmetry is $x = 1$.\nthe vertex is at $(0,0)$ and the axis of symmetry is $y = 1$.

which statement is true concerning the vertex and the axis of symmetry of $g(x)=5x^{2}-10x$?\nthe function written in vertex form is $g(x)=5(x - 1)^{2}-5$. the vertex is at $(1,-5)$ and the axis of symmetry is $x = 1$.\nthe vertex is at $(1,-5)$ and the axis of symmetry is $y = 1$.\nthe vertex is at $(0,0)$ and the axis of symmetry is $x = 1$.\nthe vertex is at $(0,0)$ and the axis of symmetry is $y = 1$.

Answer

Explanation:

Step1: Convert to vertex - form

For a quadratic function $y = ax^{2}+bx + c$, the vertex - form is $y=a(x - h)^{2}+k$, where $(h,k)$ is the vertex. Given $g(x)=5x^{2}-10x$, factor out the leading coefficient: $g(x)=5(x^{2}-2x)$. Complete the square inside the parentheses. $x^{2}-2x=(x - 1)^{2}-1$. So $g(x)=5((x - 1)^{2}-1)=5(x - 1)^{2}-5$.

Step2: Identify the vertex and axis of symmetry

For a quadratic function in vertex - form $y=a(x - h)^{2}+k$, the vertex is $(h,k)$ and the axis of symmetry is $x = h$. Here, $h = 1$ and $k=-5$, so the vertex is $(1,-5)$ and the axis of symmetry is $x = 1$.

Answer:

The function written in vertex form is $g(x)=5(x - 1)^{2}-5$. The vertex is at $(1,-5)$ and the axis of symmetry is $x = 1$.