Question

graphing quadratic functions
graph this function: ( f(x) = x^2 - 4x - 5 )
step 1: identify ( a ) and ( b ).
( a = ), ( b = )

Explanation:

Step1: Match to standard quadratic form

Standard quadratic form: $f(x)=ax^2+bx+c$.
For $f(x)=x^2-4x-5$, we get $a=1$, $b=-4$.

Step2: Find vertex x-coordinate

Vertex $x$-value formula: $x=-\frac{b}{2a}$
$x=-\frac{-4}{2\times1}=2$

Step3: Find vertex y-coordinate

Substitute $x=2$ into $f(x)$:
$f(2)=(2)^2-4(2)-5=4-8-5=-9$
Vertex: $(2, -9)$

Step4: Find x-intercepts

Set $f(x)=0$:
$x^2-4x-5=0$
Factor: $(x-5)(x+1)=0$
Solutions: $x=5$, $x=-1$
Intercepts: $(5,0)$, $(-1,0)$

Step5: Find y-intercept

Set $x=0$:
$f(0)=0^2-4(0)-5=-5$
Intercept: $(0,-5)$

Step6: Create value table

$x$	$y$
$0$	$-5$
$2$	$-9$
$4$	$-5$
$5$	$0$

Answer:

1. $a=1$, $b=-4$
2. Key points to graph: $(-1,0)$, $(0,-5)$, $(2,-9)$, $(4,-5)$, $(5,0)$; plot these points and draw a smooth upward-opening parabola through them.