Question

What attributes of the representative model of the parabola can be determined from the standard form

Answer 1

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:

$f(x) = ax^2 +bx+c$

Where a,b and c are real numbers with $a \neq 0$.

Some features that we can identify from the standard form are:

If$a>0$  the parabola opena upward.

If $a$ the parabola open downwards.

We can find the axis of symmetry . And is defined as $x = - \frac{b}{2a}$

The x intercepts are given by:

$x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}$

We can find the x intercept with the following formula:

$x = -\frac{b}{2a}$

And for the y intercept we just need to use x=0 and we got $y=c$

And for the y intercept we just need to replace the x intercept into the equation like this:

$y = a( -\frac{b}{2a})^2 + b( -\frac{b}{2a})+c$

From the standard from we can also find the domain and range. The minimum or maximum value. And we can also find the focus.