Respuesta :
Answer:
Vertex (h,k)
X intercepts and Y intercepts
Focus
Axis of symmetry
Maximum or minimum value
Step-by-step explanation:
The general form for a parabola or a quadratic function is given by:
[tex]f(x) = ax^2 +bx+c[/tex]
Where a,b and c are real numbers with [tex]a \neq 0[/tex].
Some features that we can identify from the standard form are:
If[tex]a>0[/tex] the parabola opena upward.
If [tex]a<0[/tex] the parabola open downwards.
We can find the axis of symmetry . And is defined as [tex]x = - \frac{b}{2a}[/tex]
The x intercepts are given by:
[tex]x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
We can find the x intercept with the following formula:
[tex]x = -\frac{b}{2a}[/tex]
And for the y intercept we just need to use x=0 and we got [tex]y=c[/tex]
And for the y intercept we just need to replace the x intercept into the equation like this:
[tex]y = a( -\frac{b}{2a})^2 + b( -\frac{b}{2a})+c[/tex]
From the standard from we can also find the domain and range. The minimum or maximum value. And we can also find the focus.
