Identify and sketch the graph of the following equations in R³ (a) x² + 2y² +2². 8x + 12y2z + 35= 0 (b) z = = 1- e y² (c) = 1. Show the traces as well. 9 4

Q: Given the quadratic equation y=x² + 4x-5 a. Write the equation in the form a(x + h)²+k b. Determine…

A: The given equation y=x2+4x-5. We have to write the equation into vertex form and find its…

Q: 2. Write the given equation below in standard form. 4x2 + 3y + 6y = 9 (y+1)? =D1 *+ (y+1)? = 1…

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Q: ine the graph of the paraboloid z=x2+9y2. Choose the correct graph of the equation.

A: Given the paraboloid equation is                           z=x2+9y2.

Q: Find the change of variable x = Py that transforms the quadratic form xTAx into yTDy as shown 2x? +…

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Q: 3. Find the vertex for the parabola 4x + 2y² + 8 = 0. (a) (0, -2) (b) (-2,0) (c) (2, 2) (d) (-2,1)

A: The equation of the parabola is  4x+2y2+8=0

Q: 1. Convert the following difference equation into a first-order form: Yt = Yt-1 + 2yt-2(Yt-3 – 1)

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Q: 9. Find the vertex and focus of the parabola whose equation is 24x = -(y – 6)² + 192 O V(-8, –6),…

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Q: O O 2. The graph of the equationx + 3y = 6 intersects the y-axis at the point whose coordinates are…

A: To find the intersection point

Q: Group 2 x2 – 2r – 3 c(x) = x2 – 4x – 5 11 %3D 10 8 2. Fill the Table: 3. Graph the function: 4 3 2…

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Q: Q2: A particle move on the path has parabola shape with equationf (x) = a + bx + cx²; Find the…

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Q: 3. Recall that the surfaces x² + y² = sin²(z) and x² + y² = (ln(z))² are called surfaces of…

A: As per policy the first three subparts of a question can be answered. For the rest of the parts,…

Q: Sketch and identify the graph of the equation x² + y² – 2y – 3 = 0 in 3D.

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Q: transform y=x²+12x+32 into its vertex form and give the valuesof h and k

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Q: Complete the square for each of the following quadratic forms

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Q: Another constraint you can use to compute cubic splines is that the second derivatives of adjoining…

A: Consider the cubic polynomial  fx=⋮ai-1x3+bi-1x2+ci-1x+di-1, x∈(xi-1,xi]aix3+bix2+cix+di…

Q: Write the following equation in vertex form: y2-20y+ 100 = 6x O (v-20)² = 6x O (-10)² = 4()(x-0) O…

A: Given query is to write the equation in vertex form.

Q: 5 Describe the transformation that maps the graph: 2x² - 2x + 3 a y = 2x² - 4x - 5 onto the graph y…

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Q: Identify the graph of 3x2 - 2√3xy + y2 + 2x + 2√3y = 0.

A: The given curve is 3x2 - 2√3xy + y2 + 2x + 2√3y = 0. using any graphing calculator, sketch the graph…

Q: Find the equation of the parabola, y = ax2+bx+c, that passes through the points (−1, 6), (1, 4),…

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