All Algebra 1 Resources
Example Question #1 : Parabolic Functions
What is the minimum possible value of the expression below?
The expression has no minimum value.
We can determine the lowest possible value of the expression by finding the -coordinate of the vertex of the parabola graphed from the equation . This is done by rewriting the equation in vertex form.
The vertex of the parabola is the point .
The parabola is concave upward (its quadratic coefficient is positive), so represents the minimum value of . This is our answer.
Example Question #32 : Functions And Lines
What is the vertex of the function ? Is it a maximum or minimum?
The equation of a parabola can be written in vertex form: .
The point in this format is the vertex. If is a postive number the vertex is a minimum, and if is a negative number the vertex is a maximum.
In this example, . The positive value means the vertex is a minimum.
Example Question #1 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3
Which of the graphs best represents the following function?
None of these
The highest exponent of the variable term is two (). This tells that this function is quadratic, meaning that it is a parabola.
The graph below will be the answer, as it shows a parabolic curve.
Example Question #2 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3
What is the equation of a parabola with vertex and -intercept ?
From the vertex, we know that the equation of the parabola will take the form for some .
To calculate that , we plug in the values from the other point we are given, , and solve for :
Now the equation is . This is not an answer choice, so we need to rewrite it in some way.
Expand the squared term:
Distribute the fraction through the parentheses:
Combine like terms:
Example Question #5 : Understand Linear And Nonlinear Functions: Ccss.Math.Content.8.F.A.3
None of the above
moves the parabola by units to the right.
Similarly moves the parabola by units to the left.
Hence the correct answer is option .
Example Question #1 : How To Graph A Quadratic Function
Which of the following graphs matches the function ?
Start by visualizing the graph associated with the function :
Terms within the parentheses associated with the squared x-variable will shift the parabola horizontally, while terms outside of the parentheses will shift the parabola vertically. In the provided equation, 2 is located outside of the parentheses and is subtracted from the terms located within the parentheses; therefore, the parabola in the graph will shift down by 2 units. A simplified graph of looks like this:
Remember that there is also a term within the parentheses. Within the parentheses, 1 is subtracted from the x-variable; thus, the parabola in the graph will shift to the right by 1 unit. As a result, the following graph matches the given function :