SOLUTION: Use completing the square to write the following equations in vertex form. State the vertex and whether the parabola has a maximum or minimum value. (4 marks each) y=x2−10x+

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use completing the square to write the following equations in vertex form. State the vertex and whether the parabola has a maximum or minimum value. (4 marks each) y=x2−10x+      Log On


   

Question 1006546: Use completing the square to write the following equations in vertex form. State the vertex and whether the parabola has a maximum or minimum value. (4 marks each)
y=x2−10x+3
y=−x2+12x+2
y=4m2+32m+33
The height, h metres, of a flare as a function of time, t seconds, since the flare was fired from a boat, can be modeled by the function: (5 marks)
h=−5.25(t−4)2+86
What was its height when it was fired?
What was the maximum height of the flare?
What was the time when the flare reached its maximum height?
How many seconds after it was fired did the flare hit the water?
The path of a soccer ball can be given by the quadratic function :
h=29.4t−4.9t2, where t is the time in seconds and h, is the height in metres.
Put the function in vertex form and state the maximum height reached by the ball.
How many seconds did it take to reach this height?
A police officer is investigating a crime which occurred in a rectangular field next to a building. He wants to seal the three sides of the area around the scene with 300 m of yellow police tape. What is the maximum area that he can enclose and what are the dimensions of this area? (Hint: Draw a picture and introduce a variable x for the width…think about an expression for the length in terms of x) (6 marks)
A parabola passes through the point (3, 5) on its way to the vertex at (7, 11). Determine the equation in vertex form that represents this parabola. (3 marks)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Too many different questions for one request posting for help. The quadratic equations ones can all be solved symbolically first, and then each equation can be treated according to the symbolic form you found.

To do this, try checking the lesson: Completing the Square for Solving Quadratic Equation

Start with general form y=ax^2+bx+c, complete the square, and change into Standard Form, and KEEP all the same variables as are in the general form. No real advantage in solving four exercises individually instead of solving one exercise ONE time, and then making the substitutions for each afterward. Read the vertex and line of symmetry from the finished individual equations. Vertex as Max or Min is indicated by the sign on the square term.