Which function represents a downward-opening parabola?

Which function represents a downward-opening parabola?

• A. h(x) = 10x^2 - 5
• B. h(x) = -10x^2 + 5
• C. h(x) = 10x - 5
• D. h(x) = -10x + 5

Answer: (B)

The function that represents a downward-opening parabola is determined by the coefficient of the squared term in a quadratic function (in the form of \( h(x) = ax^2 + bx + c \)). When the coefficient \( a \) is negative, the parabola opens downwards. In the function provided, \( h(x) = -10x^2 + 5 \), the coefficient of \( x^2 \) is \(-10\), which is indeed negative. This indicates that the parabola opens downward. The other functions either have a positive coefficient for \( x^2 \) or do not include a squared term at all, which would instead result in linear equations that do not form a parabola. Therefore, this reasoning supports that the function representing a downward-opening parabola is the one with the negative coefficient.

The function that represents a downward-opening parabola is determined by the coefficient of the squared term in a quadratic function (in the form of ( h(x) = ax^2 + bx + c )). When the coefficient ( a ) is negative, the parabola opens downwards.

In the function provided, ( h(x) = -10x^2 + 5 ), the coefficient of ( x^2 ) is (-10), which is indeed negative. This indicates that the parabola opens downward. The other functions either have a positive coefficient for ( x^2 ) or do not include a squared term at all, which would instead result in linear equations that do not form a parabola. Therefore, this reasoning supports that the function representing a downward-opening parabola is the one with the negative coefficient.