Question

determine the features of a quadratic function that are most easily identified by the different forms of f(x) shown in the table.
drag the feature or features for each form into the table.

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

axis of symmetry
extreme value
y-intercept
zeros

Explanation:

Step1: Analyze factored form

The factored form \( f(x) = a(x - r)(x - s) \) has roots (zeros) at \( x = r \) and \( x = s \), so the feature easily identified here is zeros.

Step2: Analyze vertex form

The vertex form \( f(x) = a(x - h)^2 + k \) has its vertex at \( (h, k) \). The extreme value (maximum or minimum) occurs at the vertex, and the axis of symmetry is \( x = h \). So extreme value and axis of symmetry are easily identified here.

Step3: Analyze standard form

The standard form \( f(x) = ax^2 + bx + c \) has the \( y \)-intercept at \( (0, c) \) (since plugging \( x = 0 \) gives \( f(0)=c \)), so the \( y \)-intercept is easily identified here.

Answer:

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