Question

Write the quadratic function in standard form. f(x) = −2x2 − 8x f(x) = Give the vertex. (x, y) = Find the intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) =

Answer 1

`f\mleft(x\mright)=-2\left(x+2\right)+8`
`\begin{gathered} x-\text{ intercept: \lparen-4,0\rparen \lparen0,0\rparen} \\ y-intercept:\text{ \lparen0,0\rparen} \\ \text{ Vertex: \lparen-2,8\rparen} \end{gathered}`

Explanation:

The quadratic function in standard form is represented as:

`ax^2+bx+c=0`

Therefore, for the given function:

If the vertex is (-2,8) the equation would be represented as;

`\begin{gathered} f(x)=a(x+2)^2+8 \\ \text{ Use one of the given points on the graph:} \\ x-\text{ intercept: \lparen-4,0\rparen \lparen0,0\rparen} \\ y-intercept:\text{ \lparen0,0\rparen} \end{gathered}`
`\begin{gathered} 0=a(-4+2)^2+8 \\ 0=4a+8 \\ 4a=-8 \\ a=-(8)/(4)=-2 \end{gathered}`

Hence, the function of the quadratic in standard form is represented as:

`f\mleft(x\mright)=-2\left(x+2\right)+8`