Intro Calculus Question..Please help me?

Question

Question 1: For the following straight lines determine the gradient and y-intercept

a) the line which passes through the origin inclined at an angle of 83° to the
positive x-axis

b) x=-8

Question 2: Rewrite the following equations in standard quadratic form (show working)

a) 3x^2-5x+2y=0
b) y-3 / x+2 =2x-1

Note: part b the 1st part before the quals sign is a fraction y-3 / divided by x+2

Question 3:
Write the equation of the line of symmetry of each of the following quadratic functions
a) y=2x^2-7x+15
b) 2y-5x+1=9x^2

Question 4:
Write each of the following functions in completed square form-show working where necessary
a) y=x^2+8x-1
b) y=2x^2-6x+7

Note: Please explain them to me if possible and write down the working if possible. the symbol ^ is the power of and / is divide by. Thankyou for helping me.

I have done most of these questions. I am just making sure I got them correct.

Answer 1

Katie, I decided to answer your math question as well. I hope you don’t mind.

Question 1
I think the term of ‘gradient’ is used in place of a term ‘slope’.

a)If it passes through the origin then your y-intercept is 0 and so is x-intercept.
The slope m= (y2-y1)/(x2-x1)= tan(angle)= tan(83)= 8.14
You can write an equation for your line in general as y=mx+b
Since b=0
y=8.14x

b)X=8
y=8.14 x 8=65.12

Question 2.
a) 3x^2-5x+2y=0
y=(3/2)x^2-(5/2)x

b) y-3 / x+2 =2x-1 I think you meant
(y-3) /(x+2) =2x-1
y -3 =2x^2 – x + 4x -2
y = 2x^2 +3x +1


Question 3:
Write the equation of the line of symmetry of each of the following quadratic functions
a) y=2x^2-7x+15
The line of symmetry is parallel to the y-axis at x1 X= x1+(x1+x2)/2 (just compute the roots (http://en.wikipedia.org/wiki/Quadratic_equation))

b) 2y-5x+1=9x^2
y=(9x^2 +5x -1)/2
solve similarly to (a)


Question 4:
Write each of the following functions in completed square form-show working where necessary
a) y=x^2+8x-1

Find the the roots see ref (http://en.wikipedia.org/wiki/Quadratic_equation)
Put it in a form y=(x+a)(x+b) where a and b are the roots satisfying the equation.

b) y=2x^2-6x+7
same as (a)


Have fun!

Answer 2

a million) there's an endless kind of a risk strategies. One risk is: y = a million / (x - 6) - discontinuous on the vertical asymptote. in case you desire "in actuality an commencing " contained interior the graph, proper right here we pass: y = (x^2 -5x - 6) / (x - 6) (the graph of this function is a in the present day line y = x + a million with a "little circle" (discontinuity) at x = 6 2) f(0) = 3, f(3) = -15 => the secant line is going by employing (0, 3) and (3, -15). subsequently the equation of the secant line is: y = -6x + 3. The slope is -6 3) i do no longer understand what "the 4 step technique" is. Sorry. The slope of the tangent line is the by employing-product at x = 3 f '(x) df/dx = -4x => f ' (3) = -12 <===== it truly is the slope of the tangent line.

Answer 3

You'll never understand these problems if you don't take the time to do them yourself. It's better to ask your teacher for help, otherwise it's just another form of cheating.