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The graph of y = x2 is shown below. Using complete sentences, explain how the graph
To solve this problem, you have to break down the equation into parts and figure out how each piece affects the picture. It is a good idea to use the point-slope formula which is y=a(x-h)2+k and break it down by variable.
a: This is the slope. Since this slope is negative, the parabola will be facing down. With a slope of 2, the parabola will be much narrower because it is covering 2 vertical blocks to 1 horizontal block on the grid, therefore it will be twice as tall as it is wide.
(h,k) is the vertex of the parabola or the point that is in the middle (in this case it is the highest point on the parabola since the parabola is facing downward).
h: -3 represents the vertex being three blocks to the left of the origin with regards to the x-axis.
k: 1 represents that the vertex is one block above the origin with regards to the y-axis.
The graph of y = x2 is shown below. | Wyzant Ask An Expert – Using complete sentences, explain how the graph of y = -2(x + 3)2 + 1 would differ from this parabola? The graph shows a parabola opening up with a vertex at 0 comma 0.For better graph take a couple of control points: `(1,1),(1,1/2),(4,1/4)`. Since function is odd, reflect it about origin. Shift the function 1 unit to the right. So, derivative equals 0 when `x=-0.41,x=2.41`. According to method of intervals number line is divided by stationary points on three intervals.OK. Show Ads. x = how far along. m = Slope or Gradient (how steep the line is). b = value of y when x=0. How do you find "m" and "b"? b is easy: just see where the line crosses the Y axis.
Steps for Sketching the Graph of the Function on eMathHelp – the graph of y = ax^2 + bx + c is shown below. determine the solution set of 0 = ax^2 + bx + c. the graph of y = x^2 has been translated 7 units to the left. the equation of the resulting parabola is _.Connect and share knowledge within a single location that is structured and easy to search. Learn more. The graph of $y=f(x)$ is shown below. Graph the following functions. Ask Question.Use graphs to solve optimisation problems. Investigate the absolute value function. Plot families of graphs and describe their characteristics. Plot the graphs of functions and their inverses by interchanging the roles of x and y. Find the relationship between the graph of a function and its inverse.
Equation of a Straight Line | Now Play With The Graph ! – …Part (B) Differentiating implicitly using the chain rule and product rule we get: 2(x^2+y^2)(2x+2ydy/dx) = (4x^2)(dy/dx) + (8x)(y) We don't need to find an explicit expression for dy/dx, just its value when x=+-1 and y=1. Substituting x^2=1 and y=1 gives: 2(1+1) How do you show a line is a tangent to a curve?Shifting the graph vertically upwards by 4 units gives the graph of y = x^2 + 2x + 5. y = x^2 is transformed to y = x^2 + 2x + 5 by shifting it horizontally to the left and vertically upwards. Approved by eNotes Editorial Team.Free functions and graphing calculator – analyze and graph line equations and functions step-by-step.