In studios and on stages, cardioid microphones are often preferred for the richness they add to voices and for their ability to reduce the level of sound from the sides and rear of the microphone.Suppose one such cardioid pattern is given by the equation(x2+y2-x)2=x2+y2. (a) Find the intercepts of the graph of the equation. (b) Test for symmetry with respect to the x-axis,y-axis,and origin.

Q: On one set of coordinate axes, graph the family of parabolasf(x) = x2 + 2x + c for c = - 3, c = 0,…

A: Solution:given f(x) = x2 + 2x + c for c =- 3, c = 0, and c = 1To describe the characteristics of a…

Q: Find the intersection points of the parabola above and the line -x+y=-4.

A: Given equation of parabola and the line are as below.

Q: 11. For the equation y = x – 9x, determine the intercepts and test for symmetry.

A: Given, y=x3-9x

Q: How can we find the slope of the parabola y?

A: You can’t find the slope of the parabola y , because a parabola is not a line. You can find the…

Q: Find the equation of a line which has y-intercept 4,and is parallel to the line 2x3y-7=0,Find the…

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Q: I need help with finding vertex,y-intercept, but I would like to double check my x-intercept answer.…

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Q: Match the equation to its graph. x=k, k<0

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Q: is the graph of y=1/2x+4/3 perpendicular to the gragh of y=-1/2x+4/3

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Q: A parabola has an equation of axis of symmetry as x = 3, and it's optimal value is (-7) if the…

A: Axis of symmetry is:  x = 3 Optimal value is:  - 7 Therefore the vertex of the parabola is:  (h, k)…

Q: Find the intercepts on the axes, test for symmetry, plot an adequate number of points, and draw the…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: If the axis of symmetry of a parabola is given by x = 4, is it possible for the directrix to have…

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Q: Find the standard equation of a parabola that has a vertical axis and satisfies the given…

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Q: On one set of coordinate axes, graph the family of parabolas f(x) = x2 + bx + 1 for b = - 4, b = 0,…

A: Consider the given general form of the equation. fx=x2+bx+1 Put b=-4 in the equation. fx=x2−4x+1 Put…

Q: Match the equation with its graph. x2 + y2 + z2 = 25

A: According to question,Given equation,x2 + y2 + z2 = 25

Q: In Problem,list the intercepts and test for symmetry with respect to the x-axis,the y-axis,and the…

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Q: (i) Sketch the graph of y =|5x²– 14r – 3| graph meets the coordinate axes.

A: Given: y=5x2-14x-3 To express: (i) The given function in the form of p(x+q)2+r form. To sketch: (ii)…

Q: 4. The equation of a family of circles with center an the y-axis is 5. The equation of a family of…

A: Topic:- geometry  Note:- as per our guideline if more than one question uploaded than only first…

Q: Match the equation with its graph. x2 - y2 + z2 = 2

A: Solution:-

Q: Match the equation with its graph. = 1 16

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Q: Find the point on the graph of the equation 16x = y2 that is closest to the point (6, 0).

A: The function is 16x=y2 and the point is 6,0.

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Given: The parabola has its vertex at the origin and  Directrix has y - intercept 8. We have to find…

Q: The roots of the equation x² - 6x + I = 0 are? The equation of the line of symmetry to the curve y…

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Q: Match the equation with its graph. y2 = 4x2 + 922 %3D 3 2-

A: This is the problem of 3 dimensional curve plotting. Based on the online available graph plotter we…

Q: The equation of the parabola that has a vertical axis of symmetry, touches the line y= 6 and has its…

A: Your 3rd option is your correct option...detailed solution I have done step by step in…

Q: If the equation y = 2x – 5x + 3 is graphed in the - xy-plane, what is the value of its y-intercept?

A: Given,            y=2x2 - 5x + 3

Q: For the parabola y=-4(x+1)^2 - 3, the range is...?

A: For  y=ax2+bx+c  with vertex      (x1  y1)

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: A parabola has its turning point at x = -4 and one of the x-intercepts is x = -3. What is the x…

A: Given Data: The x coordinates of the turning point of the parabola is: x=-4 One of the x-intercepts…

Q: A concert stage has a parabolic roof. The front edge of the roof is defined by the  equation h(x)=…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: Graph the curves and show that the 2x2-y2=C is a solution to yy'-2x=0.

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Q: Match the equation with its graph. x2 y2 z2 = 1 16 56y 3 2- -3t 3 544 +

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Q: Match the equation with its graph. y2 - 4x2 + 9z2 %3D -3 32

A: Given that: y2=4x2+9z2

Q: What is an equation of the axis of symmetry of the graph of the parabola y = 2x² + 3x + 5? A y=-} O…

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Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

Q: Match the equation with its graph. x2 y2 z2 + = 1 9 9 16 4 -5

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Q: First, graph the equation and determine visually whether it is symmetric with respect to the x-axis,…

A: Given: -

Q: Suppose the graph of y = 5x + 7x – 2 is stretched horizontally by a factor of 4. The equation of the…

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Q: If the parabola whose equation is x = ay2 + by + c has its vertex at (3,2) and a&gt; 0, then it has…

A: The given statement is that" if a parabola whose equation is x=ay2+by+c has its vertex at 3,2 then…

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: 9. If you were to graph f (x) = 2x2 + 4x – 6 , what would the coordinates of the vertex be? What…

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Q: Which is true of the graph of the parabola whose equation is y = x - 2x - 8? The x-intercepts are at…

A: Answer

Q: 1. Describe an algebraic method for determining the x-intercepts, if any, of a parabola which…

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Q: Is the graph of r(x) = -8x3 – 7x² + 2x +3 concave up or down at the point with r-coordinate –2?…

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Draw the graph of 4x - 3y = 9 by first changing the equation to Slope-Intercept Form. %3D

A: we have to draw the graph of 4x-3y=9 by first changing the equation to slope intercept form. as we…

Q: Find the points of intersection of the graphs of the equations                           x2 + y2 =…

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Q: Sketch the graph of 9x2 + 4y2 = 25, and find the foci.

A: Given equation is 9x2+4y2=25. To sketch the graph and find the foci. Solution: Given equation can be…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.