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 $f(x)$ can be found using the fact that it intersects the $x$-axis at $(1,0)$ and $(4,0)$, meaning $x=1$ and $x=4$ are its roots. Thus, the function can be expressed as $f(x) = a(x-1)(x-4)$. Since it intersects the $y$-axis at $(0,4)$, when $x=0$, $f(x)=4$. Plugging $x=0$ into the equation gives $4 = a(-1)(-4)$, leading to $a=1$. Therefore, the function is $f(x) = (x-1)(x-4) = x^2 - 5x + 4$.

Find the Quadratic Function fff Whose Graph Intersects The xxx -Axis At (1,0)( 1,0 )(1,0)

Find the Quadratic Function $f$ Whose Graph Intersects The $x$ -Axis At $( 1,0 )$