Q: Find the vertex, focus, and directrix of the parabola and sketch its graph, for the following equation: - x? + 2x + 12y - 23 = 0

Q: Find the equation of the axis of symmetry of the following parabola using graphing technology. y =…

A: y=-3x2-18x-39 The graph is,

Q: Find the coordinates of the vertex and the focus for the parabola given by the following equation:…

A:

Q: or the given equation of a parabola, determine the focus, vertex, and directrix. (x – 3)? = 32(y+ 4)…

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Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola 23.12x=y^2

A: Given: The parabola is 23.12x=y2.   Calculation: Comparing with y2=4ax, we get 4a=23.12a=5.78…

Q: Which equation represents a parabola with a vertex (-3, 2) and focus (-3,5)? O y = -3x2 + 3x + 2 O y…

A: we have to find the equation of the parabola

Q: Q4) Find the y-intercept, x-intercept(s) and the vertex point for the parabola y = x2 + 6x + 5 then…

A: Given: Parabola: y=x2+6x+5 To Find:  The y-intercept, x-intercepts and the vertex point for the…

Q: Graph the parabola. Y = (x – 4)^2 + 1. Plot five points on the parabola: the vertex, two points to…

A: Given query is to graph the parabola.

Q: Find the focus, directrix, vertex and axis of symmetry for the parabola - 12(y + 2) = (x – 2)?. -

A:

Q: For the given equation of a parabola, determine the focus, vertex, and directrix. x2 – 2x – 6y + 12…

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Q: given the equation of parabola y^2 -8x -4y -20=0,find the length of latus rectum

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Q: y=2x + 8x +9 Plot five points on the parabola: the vertex, two points to the left of the vertex, and…

A: Equation of parabola in standard form is  y = ax²+bx+c

Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola - 13.32y = z

A: We are given the parabola : -13.32y=x2 ⇒x2=-13.32y--(1) On comparing with the equation of parabola ,…

Q: use the method of completeing the sqaure to find the vertex of the parabola whose equation is…

A:

Q: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0…

Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola - 31.2x = y

A: The equation of a parabola y2=-31.2x Comparing with the standard equation y2=4ax4a=-31.2a=-7.8 Focus…

Q: Find the equation of the axis of symmetry of the following parabola using graphing technology. Y = y…

A: To find the axis of symmetry of the parabola.  y = x2 - 32x + 48.

Q: Determine the vertex, focus, directrix, and axis of symmetry of the parabola with the equation y =…

A:

Q: Find the coordinates of the vertex and the focus for the parabola given by the following equation:…

A:

Q: y = 3x? + 6x – 5

A: The given parabola is: y=3x2+6x-5...(1)

Q: For the parabola given by (y-5)2=8(x+4), find the following:(a) direction parabola opens (to the…

A: Given information:The equation of parabola is given by (y-5)2=8(x+4)

Q: Graph the parabola, then label the vertex, axis, and intercepts. 1 x²+2x + 4 4 Y = -

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Q: What is the vertex of the parabola given by the equation (y+ 1)2 =-8x?

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Q: Graph the parabola and label the vertex, axis and intercepts of Y=(-1)/4 x^2+2x+4

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Q: Find the vertex,focus,and directrix of the parabola given by y2 + 2y + 12x - 23 = 0.Then graph the…

A: y2+2y+12x-23=0⇒y2+2y=-12x+23⇒y2+2y+1=-12x+23+1⇒y+12=-12x+24⇒y--12=-12x-2 Now comparing with…

Q: (b) Find the evolute of the parabola y? = 4ax.

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Q: Q5:Cross section of a Nuclear cooling tower is in the shape of a hyperbola with equation…

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Q: Graph the parabola. y=x y3x+10x+21 Plot five points on the parabola: the vertex, two points to the…

A: See the details solution in below

Q: Determine the direction in which the parabola opens, and the vertex. y2-10y-x+23=0

A: Add x to both sides. So, this is a parabola of the form y=ax^2+bx+c with a=1=positive number. So…

Q: Find the focus of the parabola. -x- 6x+3y- 15=0 OD

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result:  Focus…

Q: graph the parabola  and determine the focus, vertex and directrix  (3y - 6)2 = 36(x - 2)  x2 + 6x…

A: As we know that the the standard equation of the horizontal parabola is: y-k2=4px-h Where:  Vertex:…

Q: Find the vertex, focus, and directrix of the parabola with the given equation, y2 - 4x - 10y + 21 =…

A: first we will write it in the general form which is (y-h)2=4a(x-k) where (k, h) are the vertices…

Q: Find an equation of the parabola with vertex , 1−4 and focus , 7−4 .

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Q: 3+ 2 Focus: (0, 2) 1+ -3 -2 -1 o -1+ -2- Directrix: y= -2 -3+

A:

Q: Find the vertex, focus, and directrix of the parabola and sketch its graph, for the following…

A: The equation of the parabola is . By simplifying the given equation of parabola it becomes,

Q: Find the vertex, focus and directrix of the parabola given by y2 + 2y + 12x - 23 = 0..Then graph the…

A: Given equation, y2+2y+12x-23=0we have to find the vertex, focus and directrix of the given equation…

Q: Use the equation x2 +18x – 2y -85 = 0 to determine the following for a parabola: a. equation in…

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Q: Q2) Put the equation (3x2 + (y – 2)2 = 3) in standard form and sketch the ellipse

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Q: For the given equation of a parabola, determine the focus, vertex, and directrix. x2 -32y

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Q: Find the vertex, focus and directrix of the parabolas whose equations are as follows: y2 + 6y + 8x +…

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Q: Find the equation of the axis of symmetry of the following parabola algebraically. 3x2 + 6x - 12 y =…

A: The equation of the parabola y=3x2+6x-12. We have to find the equation of the axis of symmetry for…

Q: What is the vertex of the parabola      y=(x-1)2-9?

A: Given the equation of parabola

Q: The equation of the parabola with center at the origin and the focus is at (0,1). A. y? = 4x B. y? =…

A:

Q: Find an equation of the parabola whose graph is shown. 14x y 7 Focus X 7

A: The given parabola is open left and symmetric about x-axis with vertex at origin. So,  The form of…

Q: Graph the parabola, then label the vertex, axis, and intercepts. 1 Y = --x² + 2x + 4 %3|

A:

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

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Q: y=(x-3)^2-1 how to find vertex and plot five point two on the left and two on the right for this…

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Q: x = ÷y² 1 4p

A: we will use basic algebraic calculations and to get p we will subtract the x-coordinate of vertex…

Q: (x – 4) = –12 (y + 3) - Find the vertex, focus, and directrix of the parabola.

A: The given equation is: x-42=-12y+3                                     (1)

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.