Find the quadratic function f whose graph intersects the x-axis at (1,0) and (4,0) and the y-axis at (0,4).
A) $f ( x ) = - x ^ { 2 } - 3 x - 4$
B) $f ( x ) = x ^ { 2 } - 5 x + 4$
C) $f ( x ) = x ^ { 2 } + 3 x + 4$
D) $f ( x ) = - x ^ { 2 } + 3 x + 4$
E) $f ( x ) = - x ^ { 2 } + 5 x + 4$

Question

Quizplus · Accepted Answer

The quadratic function that intersects the x-axis at (1,0) and (4,0) can be found using the factored form $f(x) = a(x - 1)(x - 4)$. Since it intersects the y-axis at (0,4), we have $f(0) = 4$, which gives us $a(0 - 1)(0 - 4) = 4$, leading to $a = -1$. Thus, the function is $f(x) = -(x - 1)(x - 4) = x^2 - 5x + 4$.

Find the Quadratic Function F Whose Graph Intersects the X-Axis f(x)=−x2−3x−4f ( x ) = - x ^ { 2 } - 3 x - 4f(x)=−x2−3x−4

Find the Quadratic Function F Whose Graph Intersects the X-Axis $f ( x ) = - x ^ { 2 } - 3 x - 4$