Question

2. Which quadratic function has a graph that passes through the points (-1, 4), (2, -5), and (4, 9)? A O f(x) = 0.522 - 3.5x B f(x) = -2x2 - 2 + 5 CO f(3) = 2? + 7x + 10 D. O f() = 2x2 - 5x - 3

Answer 1

The given coordinate on the graph is (-1,4), (2,-5) and (4,9).

The general form of the quadratic equation is,

`y=ax^2+bx+c`

Substituting the given coordinates in the general equaion,

`\begin{gathered} 4=a-b+c\ldots.\ldots\text{.}(1) \\ -5=4a+2b+c\ldots\text{.}(2) \\ 9=16a+4b+c\ldots.\text{.}(3) \end{gathered}`

Substracting (1) from (2),

`\begin{gathered} 3a+3b=-9 \\ a+b=-3\ldots(4) \end{gathered}`

Substracting (1) from (3),

`\begin{gathered} 15a+5b=5 \\ 3a+b=1\ldots\text{.}(5) \end{gathered}`

Substracting (4) from (5),

`\begin{gathered} 2a=4 \\ a=2 \end{gathered}`

Substituting in equation (5),

`\begin{gathered} 3(2)+b=1 \\ b=-5 \end{gathered}`

Substititing in equation (1),

`\begin{gathered} 4=2-(-5)+c \\ c=-3 \end{gathered}`

Substituting the value of a,b,c in general equation,

`y=2x^2-5x-3`

Thus, option (D) is the correct solution.