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

A quadratic function that intersects the $x$-axis at $(1,0)$ and $(4,0)$ can be represented as $f(x) = a(x - 1)(x - 4)$, where $a$ is a constant. Since it intersects the $y$-axis at $(0,4)$, substituting $x = 0$ gives $f(0) = a(-1)(-4) = 4$, which means $a = 1$. Thus, $f(x) = (x - 1)(x - 4) = x^2 - 5x + 4$.

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 $( 1,0 )$