Question

common core algebra i b - cr
quadratic functions: standard form
instruction active
calculating a vertex
consider the quadratic function:
$f(x) = x^2 - 8x - 9$
what is the vertex of the function?
vertex: $left( -\frac{b}{2a}, fleft( -\frac{b}{2a}
ight)
ight)$

Explanation:

Step1: Identify a, b in quadratic function

For \( f(x) = x^2 - 8x - 9 \), the standard form is \( ax^2 + bx + c \), so \( a = 1 \), \( b = -8 \).

Step2: Calculate x - coordinate of vertex

Using the formula \( -\frac{b}{2a} \), substitute \( a = 1 \), \( b = -8 \):
\( -\frac{-8}{2\times1} = \frac{8}{2} = 4 \).

Step3: Calculate y - coordinate of vertex

Substitute \( x = 4 \) into \( f(x) \):
\( f(4) = 4^2 - 8\times4 - 9 = 16 - 32 - 9 = -25 \).

Answer:

\( (4, -25) \)