How does the value of a affect the graph of y = ax2 if a <=0?

Q: 2. Graph using y = mx + b y = 2x – 4 8. 7. 9. Slope = 2 -5 y-intercept = - 3. 9-8 -3-2 -2 -3-

A: Y = 2x - 4 Slope = 2 Y - intercept  = -4

Q: how do i graph (steps) f(x)=x^2-4x ?

A:

Q: Describe one similarity and one difference between the graphs of x2/9 - y2/1 = 1 and (x - 3)2/9 - (y…

A:

Q: How would I graph y=f(x)+

A: Given y=f(x)+3

Q: Which points on the graph of y = 4 - x2 are closest to the point (0,2)? Ans. and

A: We will use Lagranges multiplier to find nearest points on graph

Q: Determine the concavity of the graphs of y^2=x and y=x^3

A: We have to determine the convexity of the graphs of y2 = x and y = x3 in between the points of their…

Q: 3. Which graph represents the equation below ソ=ーデマ 1 y3--x+2

A:

Q: Describe one similarity and one difference between the graphs of y2 = 4x and (y - 1)2 = 4(x - 1).

A: Consider the given functions, y2=4x and y-12=4x-1 the graph of the function y2=4x is the graph of…

Q: Which of the viewing windows would show both the x- and y-intercept of the graph of -540x+36y=3240?…

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Q: Match the portion of the graph with the corresponding equation that represents the number of…

A: We know that the general equation of the straight liney = mx + bwhere m = slopeb = constant

Q: Draw accurate graphs of y = 2x + 5, y = 2x 2 + 5

A:

Q: How do you obtain the graph of y = f(x + 2) from the graph of y = f(x)?

A: Known fact: It is known that the graph of y=fx+a,  a&gt;0 can be obtained by shifting the graph of…

Q: Write the equation for the graph. 5. 4- 2 -8 -7 -6 -5 -4 4. 1- (-1, =1) -2 (0, –2) -3 |(1, –4) -4 -5…

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Q: Find the point of intersection of the graph of the equation x2+y2=1 -x+y=1

A:

Q: What are the steps to graph (x3+2x2+x)  /  (2x2+x-1)

A: The given expression is

Q: What is the graph of y=(1/3) ^x?

A: As x approaches to infinity then limit of  y=(1/3)^x will be 0. So  optin A and option D are…

Q: how do you obtain the graph of y = f1x + 22 from the graph of y = f1x2?

A: To explain how we obtain the graph of y = f(x + 2) from the graph of y = f(x).

Q: Which is the graph of the ine y-2 = 3(x - 1)?

A:

Q: True or False To graph y = (x - 2) 3  , shift the graph of y = x3 to the left 2 units.

A: The graph y=x-23 represent the shift of the graph of y=x3 to the right 2 units.

Q: Given the graph of y = x2, how do you obtain the graph y = 4(x + 3)2 + 8?

A: Topic - transformation   of graph

Q: Sketch the graph of y = 2/(1 + x2 ).

A: Consider the given: y=21+x2Substitute x=0,y=21+0y=2Substitute x=1,y=21+1y=1Substitute…

Q: construct the graph y = x² + e ^ x.Find its lowest point

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: What is the piece-wise equation and domain for the 1t section of the graph? f(x)

A: NOTE: Refresh your page if you can't see any equations. . for the first part, the x-intercept is…

Q: Graph (x) = 2-Jx+5. 40 30 +20-

A: Here we have to graph the given function,  f(x)=2x+5

Q: What is the relation of the graph of y= x² + 9x + 14 to a real-life situation – Area, Business, or…

A: Problem: You are an engineer building a suspension bridge. Your boss asked you to develop an…

Q: Describe one similarity and one difference between the graphs of y = 4x and (y – 1) = 4(x – 1).

A: y2=4x , (y-1)2=4(x-1)

Q: The graph of y = 3(x - 2)3 + 2 always increases except at x=,

A:

Q: How many times does the graph of y = ax + b with a + 0 intersect the x-axis?

A: Given that, y=ax+b

Q: The coordinates of the turning point of the graph of y x+ 4x + q are (-2,-7). The value ofq is (1)…

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Q: How do the graphs of y = ÷ and y = compare?

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Q: How do you obtain the graph of y = f13x) from the graph of y = f(x)?

A:

Q: How do you graph x=y2 + 2y

A: The given function is, x = y2 + 2y.Consider some values for y and compute the value of x as follows.

Q: Given the graph of y = f(x), what is the value of f(0)?

A: Here we need to find the value of f(0) from given graph above.

Q: Explain the effect that the constant a has on the graph of y = ax². Be sure to consider a 0.

A: The standard equation of the parabola is (y-k)=4a(x-h)2, where (h,k) is the vertex of the parabola…

Q: How is the graph y=(x-4)^2+1 shifted relative to the graph y=x^2

A:

Q: How would you graph x is greater than or equal to 11

A: The given expression is,

Q: Sketch the graph of x − y2 = 1.

A:

Q: graph  y less than equal to x

A: To draw the graph of

Q: What causes the graph of y = x² to open downward?

A:

Q: What is the slope of the graph y = -x² at x = 3? %3D | -6 4 -4

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Q: How do the graphs of y=1/x and y=5/x+6

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Q: How will the graph of line v=-3x + 8 be affected if the 8 is changed to -3?

A:

Q: How can i graph y=-1

A: The given equation of the line is,

Q: How does the value of a affect the graph of y = ax? if a s 0?

A: The given equation is,     y=ax2

Q: If the graph of y= x is translated 5 units right, what is the equation of the new graph? Enter your…

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.