Question

1. Which quadratic has a maximum?

a. y=x2+2x+2
b. y=-2x2 – 3x+5 I
y = 0.5(x – 3)2 +1
d. y = 2x + x2 - 11

Answer 1

B

Explanation:

A quadratic has a maximum value when its leading coefficient is negative, as the parabola will be curving downwards.

For A, we have the function
`y=x^2+2x+2`

The leading coefficient here is 1, which is positive. So, A has a minimum value.

For B, we have the function
`y=-2x^2-3x+5`

In this case, the leading coefficient is -2, which is negative. So, B is curving downwards. Therefore, it has a maximum value.

Hence, B is our correct answer.

For C and D, the leading coefficient of C is 1/2 (coefficient in front of the parentheses) and the leading coefficient of D is 1 (coefficient of the squared variable). Since both are positive, both C and D have a minimum.