Which of the following quadratic functions has a graph that opens downwards?
check all that apply
A. y=2x^2-9x+3
B. y=x^2+4x+8
C. y=-(5+2x^2)
D. y=60x-15x^2
that would have to be an even power, with a negative coefficient on the highest power.
would it be c and d?
correct
To determine which of the given quadratic functions have graphs that open downwards, we need to examine the coefficient of the x^2 term.
A quadratic function in the form y = ax^2 + bx + c, where a is the coefficient of the x^2 term, determines the direction of the opening of the graph.
If a is positive (+), the graph opens upwards, and if a is negative (-), the graph opens downwards.
Let's examine each quadratic function:
A. y = 2x^2 - 9x + 3
The coefficient of the x^2 term is positive (a = 2), so the graph opens upwards.
B. y = x^2 + 4x + 8
The coefficient of the x^2 term is positive (a = 1), so the graph opens upwards.
C. y = -(5 + 2x^2)
The coefficient of the x^2 term is negative (a = -2), so the graph opens downwards.
D. y = 60x - 15x^2
The coefficient of the x^2 term is negative (a = -15), so the graph opens downwards.
Based on our analysis, the quadratic functions that have graphs that open downwards are C and D.