Question

Consider the equation f(x)=ax²+bx+c. For what values of awould the quadratic function open upward? For what values of awould the quadratic function open downward? What would happen to the function if the value of a were 0?

For the quadratic function to open upward,a would need to be
A) greater than 0
B) less than 0
For the quadratic function to open downward,a would need to be
A) less than 0
B) greater than 0
If the value of a is 0, then it would be a
A) cubic
B) linear
C) constant

Answer 1

The quadratic function f(x)=ax²+bx+c opens upward if a is greater than 0, and downward if a is less than 0. If a is 0, the function becomes a linear function.

Step-by-step explanation:

The equation f(x)=ax²+bx+c describes a quadratic function. The shape of the graph for this function is a parabola. Whether the parabola opens upward or downward depends on the sign of the coefficient a.

For the quadratic function to open upward, the value of a would need to be A) greater than 0. This is because a positive a value causes the arms of the parabola to open upwards.

For the quadratic function to open downward, a would need to be A) less than 0. A negative a value will make the arms of the parabola open downwards.

If the value of a is 0, the equation no longer describes a parabola but rather a linear function because the x² term is effectively eliminated, leaving only the linear bx term and the constant term c.