Question

question 13 (3 points)
consider the graph of ( y = ax^2 + bx + c ), where ( a = 3 ), ( b = 2 ) and ( c = -1 ). is the parabola concave up or concave down?

• concave up
• concave down

question 14 (3 points)
find the inverse of the function.
( f(x) = 5x + 3 )

• ( f^{-1}(x) = \frac{x}{5} - 3 )
• ( f^{-1}(x) = \frac{x + 3}{5} )
• ( f^{-1}(x) = \frac{x - 3}{5} )
• not a one - to - one function

Explanation:

Question 13

Step1: Recall concavity rule

For a parabola \( y = ax^2 + bx + c \), if \( a>0 \), it's concave up; if \( a<0 \), concave down.

Step2: Check \( a \) value

Given \( a = 3 \), and \( 3>0 \). So the parabola is concave up.

Step1: Start with \( y = 5x + 3 \)

To find the inverse, swap \( x \) and \( y \): \( x = 5y + 3 \).

Step2: Solve for \( y \)

Subtract 3: \( x - 3 = 5y \). Divide by 5: \( y=\frac{x - 3}{5} \), so \( f^{-1}(x)=\frac{x - 3}{5} \).

Answer:

A. Concave Up

Question 14