Question

different forms of a quadratic function reveal different features of the graph of the function.
move the words to the table to show which form of a quadratic function is best for identifying each feature.

form	feature
$f(x) = a(x - h)^2 + k$
$f(x) = ax^2 + bx + c$

zeros \t\t y-intercept \t\t extreme value \t\t axis of symmetry

Explanation:

Step 1: Analyze \( f(x) = a(x - r)(x - s) \)

This is the factored form of a quadratic function. The zeros (roots) of the quadratic are found by setting each factor equal to zero, so \( x = r \) and \( x = s \). Thus, this form is best for identifying the zeros.

Step 2: Analyze \( f(x) = a(x - h)^2 + k \)

This is the vertex form of a quadratic function. The vertex of the parabola is \( (h, k) \). The extreme value (maximum or minimum) of the quadratic function occurs at the vertex, and the axis of symmetry is the vertical line \( x = h \). So this form is best for identifying the extreme value and the axis of symmetry.

Step 3: Analyze \( f(x) = ax^2 + bx + c \)

This is the standard form of a quadratic function. To find the y - intercept, we set \( x = 0 \). When \( x = 0 \), \( f(0)=a(0)^2 + b(0)+c=c \). So this form is best for identifying the y - intercept.

Answer:

form	Feature
\( f(x)=a(x - h)^2 + k \)	extreme value, axis of symmetry
\( f(x)=ax^2 + bx + c \)	y - intercept