Question 5 Write the equation y = -3x2 18x+ 2 in vertex form. State the co-ordinates...
5. Identify the following for the quadratic relations shown. 2 3 a) co-ordinates of the vertex b) y intercept c) maximum or minimum value -20 16 12 - 20 0 6. The graph below shows the height, in meters, of a diver jumping off a springboard versus time, in seconds. a) What is the initial height of the jumper? What is this called in math terminology? b) What is the vertex? What do these numbers represent for this dive? c)...
2. (15) Give the standard form equation of the parabola with vertex = (1,2) and focus = (3, 2) b. the ellipse with center (-1,3), a focus at (-1,7) and a major axis point (1,8) c. the hyperbola with foci at (3,3), (3,-7) and vertices at (3,1), (3,-5). 3. (12) Identify the conic section and complete the square to give the standard equation given 3x2-10y +36x -20y+38 0 is 3 (24) Given the parametric equations x-Y-2, y-t,-2 4· a. Sketch...
Write down the equation of given parabola x? +8x+4y+12 =0 in standard form. State the vertex, focus and the equation of the directrix. Hence, sketch its graph. 4. Show that y² + 4y +8x + 12 = 0 represents a parabola. Hence, determine its focus, and directrix. [4 marks]
7. Write g(x) in vertex form. Then sketch the graph of g(x) g(x) = 2x + 4x - 6. Show ALL work a) Write the equation in vertex form. b) Suate the vertex -- c) State the axis-of-symmetry. a) Find the intercepts. X-intercept(s): y-intercept(s); 8. Given h(x) = x(x + 2)*(x - 2)? (1) Determine the degree and end behavior. Degree As X- As x 0 (b) Find the x-intercepts, the multiplicity of each root, and state whether the graph...
Question 12 (3 points) Match the quadratic equation with the form it represents. y = -5 (x – 3) (x + 1) 1. Standard Form 2. Vertex Form y= -x2 + 2x – 7 3. Intercept Form y=3(x + 2)2 - 1
Question 2 6 pts Find the standard form of 9x2 + 18x + y2 – 4y +4 = 0.(Remember that the conic section formulas are given at the top of this exam). (2+1) (y-2) + 1 9 O (2+1) + (0-2) = 1 0 (x + 1)² + (y - 2)² = 9 t 0 (x + 1)2 + (y - 2) =
Question 13 (5 points) A parabola has a = -2, and a vertex of (-3,2). O Explain the transformations involved, • Describe the parabola (the graph) • State the equation in the STANDARD form.
3. List the vertex form of the quadratic function and state all relevant information. 4. Convert the quadratic form f(x) +3-4 into standard form (le. multiply t out). Then check your solution to example 2. 5. Continuing with example 2, read the questions and solutions. Paying particular attention to part d. How can we find the axis of symmetry (aka the x-value of the vertex)? 6. (Note: we will not be covering 'completing the square' in this class, but feel...
2. Jane's utility function has the following form: U (1,y) = 3x2 +2.ry The prices of cand y are p, and Py respectively. Jane's income is I. (a) Find the Marshallian demands for and y and the indirect utility function. (b) Without solving the cost minimization problem, recover the Hicksian de mands for x and y and the expenditure function from the Marshallian demands and the indirect utility function. (c) Write down the Slutsky equation determining the effect of a...
Solve problem by how a,b,c,d, and e state 2. 3.5.9 (12 pts total) (a) Write the kinematic quantities F, T,ã using variables a, y as the co- (b) Draw a FBD, compute the resultant force vector, and write the vector (c) Dot your vector EOM with n to get a scalar EOM for . Integrate (d) Dot the vector EOM with ny to get a scalar EOM for j. Integrate (e) Complete the problem asked: write an expression for N...