SOLUTION: For the parabola whose equation is​ given, determine whether it opens upward or​ downward, find the​ vertex, and find the​ x- and​ y-intercepts. Then

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Question 1048919: For the parabola whose equation is​ given, determine whether it opens upward or​ downward, find the​ vertex, and find the​ x- and​ y-intercepts. Then graph the parabola.
​f(x)=x squared minus 2 x minus 48
Found 3 solutions by stanbon, MathLover1, advanced_Learner:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
For the parabola whose equation is​ given, determine whether it opens upward or​ downward, find the​ vertex, and find the​ x- and​ y-intercepts. Then graph the parabola.
​f(x)=x squared minus 2 x minus 48
---
f(x) = x^2 - 2x - 48
a = 1 ; b = -2 ; c = -48
-----
opens upward because a is positive
-------
Vertex::
x = -b/(2a) = 2/2 = 1 ; f(1) = 1^2-2*1-48 = -49
Vertex is (1,-49)
-------------------
x-intercept::
Let y = 0 ; solve for "x"::
x^2-2x-48 = 0
(x-8)(x+6) = 0
x-intercepts:: x = 8 ; x = -6
---------------------------
y-intercept::
Let x = 0 ; solve for "y"::
y = 0^2 - 2*0 - 48
y = -48
----------------
Graph::

------------
Cheers,
Stan H.
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Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

first write it in vertex form where and are and coordinates of the vertex
...complete square
.....since coefficient and , find
->->
so, we have





so, and
or and

set to find -intercepts




-intercepts are:
or
or


set to find -intercepts




which is same if you use ->
or


Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
given function
=
find
a.opens upward or downward?
b.vertex
c.x intercepts?
d.y-intercepts.
e.graph
Solution


=
a=,b=,c=
therefore,it opens upward since a= is positive.

.
=
vertex x part =
vertex=
vertex=
vertex y part =
vertex y part=
another solution by completing the square.
=
=
=- so now the function is written as vertex form
=+
so clearly
=
=

.x intercepts
=
set y= and solve for x
=
=
= or =



Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8, -6. Here's your graph:





.y intercepts
set x= and solve for
=
=
=



.graph
=
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8, -6. Here's your graph:
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