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Solving and graphing Quadratic equations

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Some homework practice I would like your assistance to prepare for exam.

1. Y^2-6y+9=8 ( exact solutions to three decimal places)
Y=_______

2. Solve 7x+x(x-4) = 0 the solution is x = _________
Find the x intercepts of f(x) = 7x+x(x-4) the x intercepts are _____

3. F(x) = -1/2x^2
The vertex is _______
Equation of the line symmetry is ________

4. (x+5)^2 = 16 ( exact and approximate solutions to 3 decimal places.

5. Write a quadratic equation. Solutions are -5, 2
Standard form ax^2+bx+c=0
The equation is __________=0

6. F(x) = -x^2+3x+28
X coordinates of the intercepts are x = ______

The y intercept is (0, ____)

7. The width of a rectangle is 3ft less than the length. The area is 4ft^2.
The width is _____ft
The length is _____ft.

8. Enclose a rectangle garden using the side of a barn as one side of the rectangle. What is the maximum area that can be enclose with a 100 ft of fence? What should the dimensions of the garden be to give this area.

The maximum area that can be enclose with a 100ft of fence is _____sq ft.
The dimensions of the garden to give this area is 50ft by ____ ft.

9. Solve by completeing the square x^2+1/2x=1
X = ________

10. Solve for x, x^2-x+2=0

11. A math book is opened to two facing pages. The product of the page numbers is 2352.

The first page is _______
The second page is ______

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Some homework practice I would like your assistance to prepare for exam.

y^2-6y+9=8 (exact solutions to three decimal places)
Y=_______

Solution: We have
y^2-6y+9=8
(y-3)^2=8
Extracting square roots, we obtain
y-3=±√8=±2√2
Adding 3 to both sides, we get
y=3±2√2
So y=3+2√2≈5.828 or y=3-2√2≈0.172

Solve 7x+x(x-4) = 0 the solution is x = _________
Find the x intercepts of f(x) = 7x+x(x-4) the x intercepts are _____

Solution: We have
7x+x^2-4x=0
x^2+3x=0
x(x+3)=0
x=0 or x+3=0
x=0 or x=-3

So the x-intercepts are (0,0) and (-3,0).

F(x) = -1/2x^2
The vertex is _______
Equation of the line symmetry is ________

Solution: We have

F(x)=-1/2 x^2=-1/2 〖(x-0)〗^2+0

So the vertex is (0,0) and the axis of symmetry is x=0.

(x+5)^2 = 16 (exact and approximate solutions to 3 decimal ...

Solution Summary

The expert examines solving and graphing quadratic equations.

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