Question

The graph of y = f(x) is shown in the xy-plane below.

Answer 1

Let's put more details in the given graph,

We will generate the equation of the graph based on the following form:

`\text{ f(x) = a(x - h)}^2\text{ + k}`

We get,

`\text{ f(x) = a(x - h)}^2\text{ + k}`
`\text{ f(x) = a(x - 1)}^2\text{ + }(-9)`
`\text{ f(x) = a(x - 1)}^2\text{ }-9`

Let's find a, use f(-2) = 0.

`f\mleft(-2\mright)=0`
`\text{ 0 = a\lbrack(-2) - 1\rbrack}^2\text{ - 9}`
`\text{ 0 = a(-2 - 1)}^2\text{ - 9}`
`\text{ 0 + 9 = a(-3)}^2\text{ - 9 + 9}`
`\text{ 9 = 9a}`
`\text{ }\frac{\text{9}}{9}\text{ = }\frac{\text{9a}}{9}`
`\text{ a = 1}`

Let's now complete the equation.

`\text{ f(x) = a(x - 1)}^2\text{ }-9`
`\text{ f(x) = (1)(x - 1)}^2\text{ }-9\text{ = (x - 1)}^2\text{ }-9\text{ }`
`\text{ f(x) = x}^2\text{ - 2x + 1 - 9}`
`\text{ f(x) = x}^2\text{ - 2x - 8}`

Therefore, the answer is letter A.