Explain the effect that the constant a has on the graph of y = ax². Be sure to consider a < 0 and a > 0.

Q: The diagram shows the curve y= 4x –x and the straight line x=4.

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Q: If the graph of y = f(x) undergoes a vertical stretch or shrink to become the graph of y = g(x), do…

A: Vertical stretches pulls the graph away from the x-axis and vertical shrinking pushes the graph…

Q: b. Find the slope of the curve at the given point. y* = 2x; (648,6)

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Q: A molecule is moving along the x-axis such that at any timet 2 0 (in seconds), its position from the…

A: Find your answer below

Q: Which of the constants in the equation f(x) = a * x ^ 2 + bx + c can be interpreted geometrically?

A: If x=0 then  f(x)=ax2+bx+cf(0)=a(0)2+b(0)+cf(0)=c This means the point is (0,c). This means the…

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: What is y-intercept of f(x)=2^z

A: The objective is to find the y-intercept of the function fx=2x

Q: Trace the curve x^3 − 6x^2 + 11x − y = 6.

A: Given- x3-6x2+11x-y=6 To draw- The graph of the above function. Concept used- The above expression…

Q: x2-5х-6 y = (х+3) (х-3)

A: y=x2-5x-6x+3x-3 We have to find the values of x at which the given y is discontinuous.

Q: write the equation of a graph that has the shape of y = under square root x but has been reflected…

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Q: Which points on the graph y = x² are closest to the point (0, 4)?

A: Since multiple questions are asked , According to guidelines I will answer the first one.

Q: s reflected in the x-axis, then the

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Q: Which points on the graph of y= 4-x^2 are closest to the point (0,2)?

A: Given function- y=4-x2 Any point on the curve of this function will be given by- x,4-x2 The given…

Q: Find the equation of the line tangent to the graph of y = 2x3 – 8x? + 3x – 6 at x = 1.

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Q: Determine the slope of the graph of 3(x2 + y2)2 = 100xy at the point (3, 1).

A: Given: 3x2+y22=100xy we know that slopem at given pointx1,y1 is given by m=dydx|x1,y1 so, we…

Q: Shows traces intercepte af + 37 + 2=0.

A: The objective is to trace x2+y2+z2+3z+2=0     ...... (1)

Q: The slope of the curve y = 5– 3x² at (-1, 2) is A. 5 С. 6 В. 2/3 D. -3

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

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Q: What point on the function y = sqrt(x + 3) is the closest to (2, 0)

A: We have to find closest to the given curve from (2, 0).

Q: Find the point at which the line ƒ(æ) = 2x intersects the line g(x) = 4x + 12

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Q: What are the graphs of the constant functions x = x0, y = y0, and z = z0 in the rectangular…

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Q: For Exercise, estimate the x- and y-intercepts from the graph. -3 – –1

A: Where the graph cuts/touch the x-axis those are the x-intercepts From the graph, we see…

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: Find the point of inflection of the curve y = 3x4– 8x3+ 6x2

A: An inflection point is a point on the graph at which the second derivative changes sign.If f…

Q: Suppose that y varies directly with x and inversley with Z, and y=28 when x=32 and z=8. Write the…

A: Directly Proportional : If a function t is directly varies (proportional) to another function s then…

Q: Find the equation of the line tangent to the graph of f(x) = 4x + 5x? – 4x – 3 at a = -7

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Q: Write the equation of the line that is tangent to the function y = xyx and is parallel to y = 2x + 1…

A: Given function,     y = x x4 Parallel line to y=2x+1Genral line is  y = mx+cOn comparing both the…

Q: Find the slope of the curve y = 2x* + 3x³ + 2x2 – 1 at a point where it crosses the x-axis

A: y=2x4+3x3+2x2-1 A curve crosses the x-axis at a point where its y-coordinate is zero. Therefore…

Q: What is the y-intercept for f(x) =;|2x + 6| – 1? А. (2,0) В. (о,-2) C. (0,6) D. (0,-1) E. not given

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Q: If the graph of y = f(x) undergoes a horizontal stretch or shrink to become the graph of y = g(x),…

A: Given that, y= f(x) is a function. f(x) will undergo a horizontal compression when the scale factor…

Q: find the slope of the curve at the point indicated y = x3 - 2x + 7, x = -2

A: Slope of the curve is determined by taking the derivative of the given function:   The given…

Q: How does the value of a affect the graph of y = ax2 if a &lt;=0?

A: It depend if a = 0 Or a is less than 0

Q: What is the graph of xy = 0? Defend your answer.

A: Given, xy=0 ⇒y=0⇒x=0

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: Find the point(s) on the graph of y = (x^2 + 3x − 1)/x where the slope is 5

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Q: Match the end behavior with the equation

A: Answer

Q: Suppose that y varies directly with x, and y= 16 when x=-2.

A: Given that y varies directly with x.

Q: Find the slope of the line that connects the points x = a and x = a + h for f(x) = 2x^2

A: Given,        The slope of the line that connects the points x=a and x=a+h for fx=2x2.

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

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Q: What point on the graph of y = x² is closest to the point (3,0)?

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Q: Trace the curve: y^2 = 4x^2 / (x+5) (x-2)

A: We want to plot the graph ofy2=4x2(x+5)(x-2)=&gt;y=4x2(x+5)(x-2) The above expression exists…

Q: Find the point on the line whose equation is 2x + y - 2 = 0  that is closest to the origin.

A: we have to find the point on the line whose equation is 2x+y-2 = 0  that is closest to the origin.

Q: y = (x-5)(x+1)

A: Given equation of curve y=x3(x-5)(x+1)                   (1) We have to trace the curve of above…

Q: does this equation define a linear function y=3/4x when x≠0

A: Linear functions are typically written in the form f(x) = ax + b The graph of Linear function  is…

Q: Sketch the graph of the solution and describe its behavior as t increases:  4y″ − y = 0,  y(−2) =…

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Q: Find the point in the curve y = x³ + 3x for which y' = y'

A: Roots of y' problem....

Q: he equation y" – F

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Q: Write an equation for a line perpendicular to f (1) = 5x – 1 passing through the point (5, 20). %3D…

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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: Use a graph to solve the equation sec x = 1 for -2π ≤ x ≤ 2π.

A: Consider the given equation, secx=1 for -2π≤x≤2π here the objective is to find the solution of the…