Question

Match each quadratic function with the attributes of its parabolic graph.

Answer 1

f(x)=-0.3(x-2)²+5

• Option A: ,The vertex, (h,k) = (2, 5)

,

• Option E: ,Axis of Symmetry, x=2

• Option I: ,The focus is (2, 4 1/6)

f(x)=0.2(x+2)²-5

• Option C: ,The vertex, (h,k) = (-2, -5)

,

• Option F: ,Axis of Symmetry, x= -2

• Option G: ,The focus is (-2, 3 3/4)

Explanation:

Part A

Given the equation:

`f(x)=-0.3(x-2)^2+5`

The standard equation of an up-facing parabola with a vertex at (h,k) and a focal length |p| is given as:

`(x-h)^2=4p(y-k)`

We rewrite the given equation in the form above:

`\begin{gathered} f(x)=-0.3(x-2)^2+5 \\ f(x)-5=-(3)/(10)(x-2)^2 \\ -(10)/(3)[f(x)-5]=(x-2)^2 \\ \left(x-2\right)^2=4(-(5)/(6))[f(x)-5] \end{gathered}`

From the form above:

• Option A: ,The vertex, (h,k) = (2, 5)

,

• Option E: ,Axis of Symmetry, x=2

`Focus,(h,k+p)=(2,5-(5)/(6))=(2,4(1)/(6))`

• Option I: ,The focus is (2, 4 1/6)

Part B

Given the equation:

`f(x)=0.2(x+2)^2-5`

Rewrite the equation in the standard form given earlier:

`\begin{gathered} 0.2(x+2)^2=f(x)+5 \\ (x+2)^2=5[f(x)+5] \\ (x+2)^2=4((5)/(4))[f(x)+5] \end{gathered}`

From the form above:

• Option C: ,The vertex, (h,k) = (-2, -5)

,

• Option F: ,Axis of Symmetry, x= -2

`Focus,(h,k+p)=(-2,-5+(5)/(4))=(-2,-3(3)/(4))`

• Option G: ,The focus is (-2, 3 3/4)