Question

which of the following is the standard form of a quadratic equation?
y = a|x| + b
y = ax² + bx + c
y = mx + b
y = a(x - h)² + k

Explanation:

To determine the standard form of a quadratic equation, we analyze each option:

• The first option \( y = a|x| + b \) is the equation of an absolute - value function, not a quadratic function.
• The second option \( y=ax^{2}+bx + c \) (where \( a

eq0 \)) is the standard form of a quadratic equation. A quadratic equation is a polynomial equation of degree 2, and in this form, the highest power of \( x \) is 2, with \( ax^{2} \) being the quadratic term, \( bx \) the linear term, and \( c \) the constant term.

• The third option \( y = mx + b \) is the slope - intercept form of a linear equation (degree 1), not a quadratic equation.
• The fourth option \( y=a(x - h)^{2}+k \) is the vertex form of a quadratic equation, not the standard form.

Answer:

B. \( y = ax^{2}+bx + c \)