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Example Questions
Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola
Determine the direction in which the following parabola opens, if the y-axis is vertical and the x-axis is horizontal:
Down
Right
Left
Along
Up
Left
In order to determine which direction the parabola opens, we must first put the equation in standard form, which can be expressed in one of the following two ways:
If the equation is for as in the first above, the parabola opens up if
is positive and down if
is negative. If the equation is for
as in the second above, the parabola opens right if
is positive and left if
is negative. Rearranging our equation, we get:
We can see that our equation is for , which means the parabola will open either left or right. The sign of the first term is negative, so this parabola will open to the left.
Example Question #1801 : Pre Calculus
Which direction does the parabola open?
Upwards
Leftwards
Rightwards
Downwards
Upwards
For the function
The parabola opens upwards if a>0
and downards for a<0
Because
The parabola opens upwards.
Example Question #3 : Determine The Equation Of A Parabola And Graph A Parabola
Determine what direction the following parabola opens:
The standard form for a parabola is in the form:
The coefficient of the term determines whether if the parabola opens upward or downward. Since the
term in the function
is
, the parabola will open downward.
Example Question #4 : Determine The Equation Of A Parabola And Graph A Parabola
Determine what direction will the following function open:
Use the FOIL method to determine in its standard form for parabolas, which is
.
Regroup the terms.
Since the coefficient of the term is negative, the parabola will open downward.
Example Question #1802 : Pre Calculus
If a parabola has vertex and focus
, which direction will it open?
right
we would need to know the directrix to determine the parabola's direction
left
up
down
up
The focus is above the vertex, which means that the parabola will open up
Example Question #1803 : Pre Calculus
Determine the direction in which the parabola will open.
Up
The graph is a straight line.
Right
Left
Down
Left
In order to determine which way this parabola, group the variables in one side of the equation. Add on both sides of the equation to isolate
.
Because the equation is in terms of , the parabola will either open left or right. Notice that the coefficient of the
term is negative.
The parabola will open to the left.
Example Question #1804 : Pre Calculus
Determine whether the following parabola opens up or down and state how you know.
Down, because the linear term is negative.
Up, because the linear term is negative.
Up, because the squared term is positive.
Down, because the constant term is negative.
Up, because the squared term is positive.
Determine whether the following parabola opens up or down and state how you know.
To determine the direction a parabola opens, we only need to worry about the squared term.
In this case, it is positive, so the parabola opens upward.
The linear term is negative, so the parabola will be to the right of the y-axis.
The constant term is negative, so the parabola will be located below the x-axis.
Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola
Determine which direction the equation opens:
In order to determine how the parabola will open, we will need to rewrite the equation in standard form.
Write the standard form for parabolas.
Subtract from both sides of the equation.
Since the coefficient of the is negative, and the equation is in terms of
, the parabola will open downward.
The answer is:
Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola
Which is the equation for a parabola that opens down?
The answer is because it is the only degree-2 polynomial with a negative leading coefficient.
Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola
Express the following equation for a parabola in standard form:
In order to be in standard form, the equation for a parabola must be written in one of the following ways:
We can see that our equation has all of the components of the first form above, so now all we must do is some algebra to rearrange the equation and express the function y in terms of x. We start by simplifying the fraction on the left side of the equation, and then we isolate y to give us the equation of the parabola in standard form:
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