Question

1. Identify the vertex of the quadratic equation y=2x2+8x-10. using the formula

2. Write the equation y=2x2+8x-10. in vertex form using the vertex found in #1.

3. Show how you can use completing the square to go from the standard form of the equation in #1 to the vertex form found in #2.

4. Explain the relationship between the solutions to the quadratic equation 0=2x2+8x-10 and the graph of the quadratic equation y=2x2+8x-10.

5. How many solutions are possible when solving the quadratic equation

6. Use the answers to #4 and #5 to make a geometric explanation of the different number of solutions possible

Answer #1

1) Solve the given quadratic equation by using
Completing the Square procedure and by
Quadratic formula ( you must do it both ways).
Show all steps for each method and put your answer in simplest
radical form possible.
4X2 + 4X = 5
2) Which part of the Quadratic Formula can help you to find the
Nature of the roots for the Quadratic Equation. Explain how you can
find the nature of the roots and provide one Example for...

[5 point] 1. Examine the quadratic relation y = -2x2 + 16x –
30.
a) Express the relation in factored form. Show your
steps.
b) Determine the zeros.
c) Determine the coordinates of the vertex.
d) Determine the y-intercept.
e) Sketch the graph of the relation.
[5 point] 2. Examine the quadratic relation y = 4x2 – 4x +
1.
a) Express the relation in factored form.
b) Determine the zeros.
c) Determine the coordinates of the vertex.
d) Determine...

1) Write the standard form of the equation of the parabola that
has the indicated vertex and whose graph passes through the given
point.
Vertex: (3, −1); point: (5, 7)
f(x) = __
2) Write the standard form of the equation of the parabola that
has the indicated vertex and whose graph passes through the given
point.
Vertex: (4, 5); point: (0, 1)
f(x) = __
3) Write the standard form of the equation of the parabola that
has the indicated...

1. Write the new function y=x^3 is reflected with respect to the
x axis, stretched by a factor of 5, shifted to the left 4 units and
shifted down 1 unit.
1a. solve by factoring
Ix^2-x-6I=6
1b. solve using quadratic formula
3x^2+2x=-1
1c. Explain how g(x) is transformed from the graph of y=x^2
The formula is g(x)=5(x+2)^2-5
Vertex coordinates is(-2,-5)

Solve the equation x^2-40x+1=0 using the quadratic formula. Use
five-digit decimal arithmetic to find numerical values for the
roots of the equation; for example, you will need (399)^(1/2)=
19.975. Identify any loss-of-significance error that you
encounter.
(b) Find both roots accurately by using only five-digit decimal
arithmetic.

1)Find the volume of the solid whose base is a circle with
equation x^2+y^2=36 and cross-sections are squares perpendicular to
the x-axis.
(a) Create the graph for this problem
(b) What is the volume of one 'slice'?
(c) What is the integral for the volume?
(d) What is the volume in exact form?
2) Find the volume of the region bounded by y=-x^2+4 and y=x+2
rotated about the line y=5
(a) Create the graph for this problem
(b) What is...

Question:
1. Can the equation x = 5 be written as slope intercept form?
Explain the reason(s).
2. What’s the relationship between two perpendicular lines in
terms of slopes? Do you think this relationship is true for the
perpendicular lines x = 0 and y =0? Why or why not?
3. How do you determine, from a graph of a function, if the
function is even, odd or neither?
4. Suppose that a function f whose graph contains no breaks...

1. Given an ellipsoid with equation
(x−5)^2 /16 +(y−10)^2/ 9+(z−6)^2/ 16= 1 and the plane with equation
y = 19 ﬁnd an equation for the curve of intersection of the two
given surfaces
2.Given vectors a and b, express the vector projection of b onto
a, indicated by p=PROJaB. Now use the decomposition b = projab +
orthab to solve for orthab, which is the vector component of b
which is orthogonal to a.

Given are five observations for two variables, x and y .
xi
1
2
3
4
5
yi
53
58
47
21
11
Use the estimated regression equation is y-hat = 78.01 -
3.08x
A.) Compute the mean square error using
equation.
s^2 = MSE = SSE / n -2
[ ] (to 2 decimals)
B.) Compute the standard error of the estimate
using equation
s = sqrtMSE = sqrt SSE / n - 2
[ ] (to 2 decimals)...

1. (5pts.) Compute the derivative dy/dx for y = 7√ 9π +
x ^5 /6 + 27e^x .
3. (5pts.) Write the equation of the tangent line to the
graph of y = 3 + 8 ln x at the point where x = 1.
4. (5pts.) Determine the slope of the tangent line to
the curve 2x^3 + y^3 + 2xy = 14 at the point (1, 2).
5. (5pts.) Compute the derivative dw/dz of the function
w =...

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