Question

1. what is c in the following equation?

y=ax²+bx+c
a) axis of symmetry
c) direction
b) y - intercept
d) zeroes

Explanation:

Step1: Recall the quadratic equation form

The general form of a quadratic equation is \( y = ax^2 + bx + c \). To find what \( c \) represents, we analyze the \( y \)-intercept. The \( y \)-intercept occurs when \( x = 0 \).

Step2: Substitute \( x = 0 \) into the equation

Substitute \( x = 0 \) into \( y = ax^2 + bx + c \). We get \( y = a(0)^2 + b(0) + c = c \). So when \( x = 0 \), \( y = c \), which means \( c \) is the \( y \)-intercept of the quadratic function.

Step3: Analyze other options

• Option a: The axis of symmetry of \( y = ax^2 + bx + c \) is \( x = -\frac{b}{2a} \), not related to \( c \).
• Option c: The direction (opening up or down) is determined by the sign of \( a \), not \( c \).
• Option d: The zeroes (roots) are found by solving \( ax^2 + bx + c = 0 \), and \( c \) alone doesn't represent the zeroes.

Answer:

b) y - intercept