In the graph below there are two points labelled 𝐴𝐴 (1, 3) and 𝐵𝐵 (2,1). Find an equation for thefollowing functions below that pass through the points A and B, sketching each on the Cartesianplane below. State your equations in the space below.a. Straight lineb. Parabolac. Cubic____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________6 marksAB
Question
In the graph below there are two points labelled 𝐴𝐴 (1, 3) and 𝐵𝐵 (2,1). Find an equation for thefollowing functions below that pass through the points A and B, sketching each on the Cartesianplane below. State your equations in the space below.a. Straight lineb. Parabolac. Cubic____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________6 marksAB
Solution
I'm sorry, but I can't provide the help you're looking for because your question is missing the graph. However, I can guide you on how to find the equations for the straight line, parabola, and cubic function that pass through the points A(1,3) and B(2,1).
a. Straight line: The equation of a straight line is given by y = mx + c, where m is the slope and c is the y-intercept. The slope between two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). So, the slope m between A and B is (1 - 3) / (2 - 1) = -2. Substituting x = 1 and y = 3 into the equation to find c, we get 3 = -2*1 + c, so c = 5. Therefore, the equation of the line is y = -2x + 5.
b. Parabola: The general equation of a parabola is y = ax^2 + bx + c. Since it passes through A and B, we can form two equations: 3 = a1 + b1 + c and 1 = a4 + b2 + c. We need a third point or condition to find a, b, and c.
c. Cubic: The general equation of a cubic function is y = ax^3 + bx^2 + cx + d. Since it passes through A and B, we can form two equations: 3 = a1 + b1 + c1 + d and 1 = a8 + b4 + c2 + d. We need two more points or conditions to find a, b, c, and d.
Similar Questions
16) The graph of a quadratic function is called:*1 pointA) a lineB) a parabolaC) a hyperbolaD) a cubic
the curve of the quadratic function f: f(x)= -ax2+bx+c is drawn on the cartesian coordinate and the vertex of the curve(3,1) the curve intersects the x-axis twice where a,b,c are constants what is the value of c ?
Graph the function labeling the vertex, y-intercept, and x-intercepts.
The graph of a function g is shown. The x y-coordinate plane is given. The curve begins at the point (−2, 0), goes up and right, passes through the point (−1.5, 1), goes up and right, changes direction at the point (−1, 1.5), goes down and right, passes through the point (−0.5, 1), goes down and right, passes through the origin, goes down and right, passes through the point (0.5, −1), goes down and right, changes direction at the point (1, −1.5), goes up and right, passes through the point (1.5, −0.5), goes up and right, changes direction at the point (2, 0.5), goes down and right, crosses the x-axis at x = 2.5, goes down and right, changes direction at the point (3, −1), goes up and right, passes through the point (3.5, −0.5), goes up and right, and ends at the point (4, 0.5). Estimate 4 −2 g(x) dx with six subintervals using the following. (a) right endpoints 0 Correct: Your answer is correct. (b) left endpoints -0.5 Correct: Your answer is correct. (c) midpoints
The graph of a function f is given in the figure.A curve is shown on the x y coordinate plane. It begins at the point (−2, −1), goes up and to the right, passes through the approximate point (−1, −0.2), and passes through the negative x-axis at the approximate point (−0.8, 0). It then continues up and right, passes through the positive y-axis at the point (0, 1), and reaches a high point at (1, 3). It then goes down and right, passes through the points (2, 2) and (3, 1), and ends at the approximate point (4, 0.5).(a)Find the value of f(1).(b)Estimate the value of f(−1).(c)For what values of x is f(x) = 1? (Enter your answers as a comma-separated list.) (d)Estimate the value of x such that f(x) = 0.x = (e)State the domain and range of f. (Enter your answers in interval notation.)domain range (f)On what interval is f increasing? (Enter your answer using interval notation.)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.