Find the Vertex, the Line of Symmetry, the Maximum Or Minimum Value of the Quadratic Function
- Give exact and approximate solutions to three decimal places. (x-9)^(2)=9
What are the exact solutions?
x = ______
(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.) There are no approximate solutions since the solutions are integers.
- Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x)=2x^(2)-8x+20
What is the vertex? ______(Type an ordered pair.)
What is the equation of the line of symmetry? ______(Type an equation.)
What is the maximum/minimum of f(x)? ______
Is the value, f(2)=12 a minimum or a maximum? ______
Create a graph that represents f(x).
- Find the x-intercepts and y-intercepts for f(x). f(x)=x^(2)-5x+5
The x-intercept(s) is(are) ______
The x-intercept(s) is(are) ______
or
There are no intercepts ______
- Give exact and approximate solutions to three decimal places. x^(2)-5x+5=0
The exact solutions are x= ______(Use radicals as needed. Use a comma to separate answers.)
The approximate solutions to 3 decimal places are x= ______(Use a comma to separate answers.)
- Graph the function. Find the vertex, line of symmetry, and maximum or minimum value. f(x)=(x+5)^(2)-4
The vertex is ______(Type an ordered pair.)
The minimum value is f(x)= ______
Create a graph.
- Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x)=3x^(2)-6x+6
The vertex is ______(Type an ordered pair.)
The line of symmetry is ______(Type an equation.)
The maximum/minimum if f(x) is ______
Is the value, f(1)=3 a minimum or maximum? ______
Create a graph.
- For the scatterplot, determine which of the following types of functions might be used as a model for the data.
1,2
3,3
5,4
7,4
9,5
Choose the best answer. A. not linear or quadratic B. quadratic C. linear
- A student opens a mathematics book to two facing pages. The product of the page numbers is 702. Find the page numbers.
The first page is _____
The second page is _____
- Find and label the vertex and the line of symmetry. Graph the function.
f(x)=-3(x+1)^(2)
The vertex is _____ (Type an ordered pair.)
The equation of the line of symmetry is _____ (Type an equation.)
Create a graph.
- Write a quadratic equation having the given numbers as solutions. -10 and -5
The quadratic equation is ______=0 (Type your answer in standard form. Type an expression using x as a variable.)
- The number of tickets sold each day for an upcoming performance of Handel’s Messiah is given by N(x)=-0.4^(2)+10x+11, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?
Ticket sales will peak _____ days after the concert was first announced.
The number of tickets sold on that day will be _____. (Round to the nearest integer.)
- Solve the formula for the given variable. Assume all variables represent nonnegative numbers. A=3s^(2), for s
What is the correct value for s?
- Solve for x. 3x^(2)=-7x-2
Elect the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. x=______(Type an integer or a simplified fraction. Use a comma to separate answers as needed.
B. There is no solution.
- Determine the nature of the solutions of the equation. y^(2)=(5)/(3)y+(2)/(5)
Choose the correct answer below.
A. The equation has two non-real solutions.
B. The equation has two real solutions.
C. The equation has one real solution.
- Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. f(x)=x^(2)=x^(2)-12x-5
What is the vertex? ______(Type an ordered pair.)
What is the equation of the line of symmetry? ______(Type an equation.)
What is the maximum/minimum of f(x)? ______
Is the value, f(6)=-41 a minimum or a maximum? ______
Create a graph that represents f(x).
- A. Solve 4x^(2)=8
What are the solutions? X=______(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
B. Find the x-intercepts of f(x)=4x^(2)-8
What are the x-intercepts? ______(Type an ordered pair. Type an exact answer, using radicals as needed. Rationalize all denominators. Use a comma to separate answers as needed.)
- Solve by completing the square. x^(2)+2x-3=0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is x=______(Use a comma to separate answers as needed.)
B. There is no solution.
- A. Solve 3x^(2)-5x-11=0
What are the solutions? x=______(Type exact answers, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.
B. Find the x-intercepts of f(x)=3x^(2)-5x-11
What are the x-intercepts? ______(Type ordered pairs. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
- Find and label the vertex and the line of symmetry. Graph the function.
f(x)=-(1)/(3)x^(2)
The vertex is ______(Type an ordered pair.)
The equation of the line of symmetry is ______(Type an equation.)
Graph the equation.
- The width of a rectangle is 4 ft less than the length. The area is 12 ft^(2). Find the length and the width.
The width is _____ ft.
The length is _____ ft.
- Find the vertex, the line of symmetry, the maximum or minimum value of f(x), and graph the function. f(x)=-(x+7)^(2)-5
The vertex is ______(Type an ordered pair.)
The line of symmetry is ______(Type an equation.)
The maximum/minimum if f(x) is ______
Is the value, f(-7)=-5 a minimum or maximum? ______
Create a graph.
- Give exact and approximate solutions to three decimal places.
y^(2)-8y+16=25
What are the exact solutions? y=______(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
There are no approximate solutions since the solutions are integers.
- Determine the nature of the solutions of the equation.
x^(2)-10x+25=0
Multiple choice: What does the equation have?
A. one real solution
B. two non-real solutions
C. two real solutions