Question

a of a quadratic function is that is determining which of the listed attributes? move the correct form into the blanks for each
attribute\tform
axis symmetry\t
vertex\t
intercepts or roots\t
concept\t
$f(x)=ax^2 + bx + c, \\, a \
eq 0$
$f(x)=a(x - h)^2 + k, \\, a \
eq 0$
$f(x)=a\left(x - r_1\
ight)\left(x - r_2\
ight)$

Explanation:

Step1: Analyze Axis of Symmetry

The vertex form of a quadratic function is \( f(x)=a(x - h)^2 + k, a
eq0 \). The axis of symmetry is given by \( x = h \), which is easily identifiable from the vertex form. So for axis of symmetry, the form is \( f(x)=a(x - h)^2 + k, a
eq0 \).

Step2: Analyze Vertex

The vertex form \( f(x)=a(x - h)^2 + k, a
eq0 \) has its vertex at \( (h,k) \), so the form that helps in finding the vertex directly is the vertex form \( f(x)=a(x - h)^2 + k, a
eq0 \).

Step3: Analyze x - intercepts or Roots

The factored form of a quadratic function is \( f(x)=a(x - r_1)(x - r_2) \), where \( r_1 \) and \( r_2 \) are the roots (x - intercepts) of the function. So to find x - intercepts or roots, we use the factored form \( f(x)=a(x - r_1)(x - r_2) \).

Step4: Analyze y - intercept

The standard form of a quadratic function is \( f(x)=ax^2+bx + c, a
eq0 \). To find the y - intercept, we set \( x = 0 \), and we get \( f(0)=c \). So the standard form \( f(x)=ax^2+bx + c, a
eq0 \) is used to find the y - intercept.

Answer:

Attribute	Form

| Axis of Symmetry | \( f(x)=a(x - h)^2 + k, a
eq0 \) |
| Vertex | \( f(x)=a(x - h)^2 + k, a
eq0 \) |

x - intercepts or Roots

\( f(x)=a(x - r_1)(x - r_2) \)

| y - intercept | \( f(x)=ax^2+bx + c, a
eq0 \) |