Question

practice with quadratic functions in stand
the graph of which function will have a maximum and a y-intercept of 4?
$f(x) = 4x^2 + 6x - 1$
$f(x) = -4x^2 + 8x + 5$
$f(x) = -x^2 + 2x + 4$
$f(x) = x^2 + 4x - 4$

Explanation:

Step1: Recall properties of quadratic functions

A quadratic function is in the form \( f(x) = ax^2 + bx + c \). The parabola opens up (has a minimum) if \( a > 0 \) and opens down (has a maximum) if \( a < 0 \). The \( y \)-intercept is found by setting \( x = 0 \), so \( f(0)=c \).

Step2: Check the coefficient \( a \) for maximum

• For \( f(x) = 4x^2 + 6x - 1 \), \( a = 4>0 \), opens up (minimum), eliminate.
• For \( f(x) = -4x^2 + 8x + 5 \), \( a = -4<0 \), opens down (maximum). Now check \( y \)-intercept: \( f(0)=5

eq4 \), eliminate.

• For \( f(x) = -x^2 + 2x + 4 \), \( a = -1<0 \), opens down (maximum). Check \( y \)-intercept: \( f(0)=4 \), which matches.
• For \( f(x) = x^2 + 4x - 4 \), \( a = 1>0 \), opens up (minimum), eliminate.

Answer:

\( f(x) = -x^2 + 2x + 4 \)