Find Algebraically the Exact Coordinates - Engineering Assignment Help

Assignment Task:

Task:

Part A a) Graph y = x-2 4x + 3 showing all important features. b) 1) Find algebraically the exact coordinates of the point(s) of intersection of y - x2 3 4x + 3 and the line ii) y —1 iii) y = —10 c) Choose two of your own vales( one positive and one negative) to repeat part b) d) Illustrate graphically your answers v_Rart b) -on another graph. e) Using your answers in part b) and c)ipredict the values of m for which the graphs of y = x2 4x + 3 and the line of the form y in havefl 0 Two points of intersection; ii) One point of intersection; Using quadratic theory and algebraic techniques to prove your predictioninsNion ppoartinist)o.f intersection. Part B  

a) Graph y 2x2 + 5x 5 showing all important features. b) Find algebraically the exact coordinates of the point(s) of intersection of y — 2x2 + 5x — 5 and the line 1) y = —2 ii) y =-- —8.125 y = —10 Illustrate graphically your answers to part b) on another graph. d) Using your answers in part b) and c) predict the values of m for which the graphs of y = 2x2 + 5x 5 and y = in have 1) Two points of intersection; ii) One point of intersection; iii) No points of intersection. e) Using quadratic theory and algebraic techniques to prove your predictions in part d). 

Part C 

a) Graph y = x2 - x + 9 showing all important features. b) On the same axes graph the line y = mx where m is equal to 
i) 0 ( i.e. y = 0); ii) 1 c) State the number of points of intersection for y = x2 - x + 9 and y 
iii) 5 iv) 7 
mx for each value in part b). 
d) Complete the table below as appropriate which shows the number of points of intersection for y = x2 x 9 and y = mx for each value of m. 

e) Using your table to propose a conjecture for the values of m for which the graphs of y — x2 — x + 9 and y mx have 
f) Part D Summarise your findings in Part A and Part B and use these to answer the following questions. a) For what values of k does the line y = kx 2 and the parabola y = 1 + 5x --- 2x2 0 touch ii) intersect iii) not intersect b) Prove that y = 2x2 --- 6x + 7 and y 2x + 3 touch each other and find the point of contact. 

i) Two points of intersection ii) One point of intersection 

iii) No points of intersection. Using quadratic theory and algebraic techniques to prove your conjecture in part.). 
 

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