Question

on the card below, select which statement is incorrect.

r(x) = x² + 2x − 35
#1: r(x) has a vertex on the y - axis.
#2: r(x) has zeros at - 7 and 5.
#3: the parabola of r(x) opens up.

○ #1
○ #2
○ #3

correct and rewrite the incorrect statement.
your answer

Explanation:

Part 1: Identifying the Incorrect Statement

• For a quadratic function \( r(x) = ax^2 + bx + c \), the x - coordinate of the vertex is \( x = -\frac{b}{2a} \). For \( r(x)=x^{2}+2x - 35 \), \( a = 1 \), \( b = 2 \), so \( x=-\frac{2}{2\times1}=- 1

eq0 \). So the vertex is not on the y - axis (y - axis is \( x = 0 \)).

• To find the zeros, set \( r(x)=0 \), \( x^{2}+2x - 35=(x + 7)(x - 5)=0 \), so \( x=-7 \) or \( x = 5 \), so statement #2 is correct.
• Since \( a = 1>0 \), the parabola opens up, so statement #3 is correct.

The original statement #1 says "r(x) has a vertex on the y - axis". We know the x - coordinate of the vertex is \( x=-1 \). So we rewrite the statement to reflect the correct position of the vertex.

Answer:

#1

Part 2: Correcting the Incorrect Statement