A quadratic function has its vertex at the point ( – 10, – 6). The function passes through the point (7, 7). When written in vertex form, the function is f(x) = a(x – h)' + k, where:

Q: For the cubic polynomial function f(x) = ax³ + bx? + cx + d, find a, b, c, and d so that 0 is a…

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Q: The table shows the mass of a substance decreasing over a period of time during a chemical…

A: Let the quadratic equation is  Mt=at2+bt+c                            ……(1) where, a, b and c are…

Q: (h) Write down the Lagrange's polynomial through (x0, fo), (x1, f1), (x2, f2). Hence express

A: h.  we have given the set of tabular values (x0,f0),(x1,f1),(x2,f2)we know that the lagrange's…

Q: Find a degree 4 polynomial that approximates the solution of y'=y+x², if y=1 when x=0. a.y=1+x+ b.…

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Q: Find the minimum value of g(t)=t3−588t+4 on the interval [−7,15]

A: We can find the minimum value as below

Q: Find the standard form f(x) = a(x – h)²+k__of the quadratic function that has zeros of 9. and and…

A: The standard form of the quadratic function is f(x)=a(x-h)2+k. This form has zeros at 15 and 95.…

Q: Evaluate the quadratic form f(x) = xT Ax for the given A and x.

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Q: If y=f(x) is an odd polynomial function, which of the following is an odd polynomial functions?…

A: Given y=f(x) is odd polynomial  a polynomial is said to be odd if f(-x)=-f(x)

Q: The table gives the increase or decrease in the number of donors to a college athletics support…

A: a) Let t=0 for the year 1985, Rewrite the given data as shown below, Year Rate of change 0 -164…

Q: 6 Match the following quadratics to their zeros. x² + 10x + 21 = 0 x² + 76x + 75 = 0 x² + 32x + 31 =…

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Q: Find the degree 3 Taylor polynomial T3 (x) of function f(x) = (-7x + 46)³/2 %3D at a = 6. T3(x) =

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Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

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Q: 1. If the roots of the quadratic function f(x)=x²+2x+1 are to be obtained by paper folding, exactly…

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Q: Find a quadratic function F(x) that takes its largest value of 300 at x = 2, and express it in…

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Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3 7. y=f(x)…

A: If y=fx takes the values y0,y1,....,yn corresponding to x0,x1,....,xn then the Lagrange's…

Q: Evaluate the quadratic form f(x) = xT Ax for the given A and x.

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Q: On a cosine function y=Acos(Bx)+C, which of the following expressions will always calculate the…

A: The cosine function is  y=Acos(Bx)+C

Q: Find the cubic polynomial function p(x) = a + bx + cx² + dx³ such that p(1) = 1, p'(1) = 5, p(-1) =…

A: p(x) = a+ bx + cx2 + dx3 p(1) = 1p'(1) = 5p(-1) = 3p'(-1) = 1

Q: Let (-1,(-1) = 2), (0, ƒ(0) = 5) and (1, f(1) = 6). Which one gives quadratic spline functions?…

A: Given, -1,f(-1)=2,(0,f(0)=5) and 1,f(1)=6

Q: 6.6 Determine the lowest real root of f(x) = -12 - 21x + 18r - 2.4x: (a) graphically and (b) using…

A: Consider the given equation. fx=-12-21x+18x2-2.4x3 Now, make the table to find the values of the…

Q: An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A: As we are making a box, its height must be greater than 0. So we have x>0. As the width of the…

Q: 8. The graph that could represent a fifth degree polynomial of the form y = ax+ bx + cx + dx² + ex +…

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Q: IB) Find the cnber of curvatee, eguation of the curde of cuuunfure f (x)> Jax of the gmph. of at x=…

A: Consider the given curve as, fx=2x at, x=4 Let y=fx=2x

Q: The quadratic function f(x) = a(x – hỷ² + k, a + 0, form. The graph of f is called a/an whose vertex…

A: A quadratic function is a second-degree polynomial function and the general form of a quadratic…

Q: 15(a). Consider the quadratic function f(x)=x²-2x-3. (1) Find the vertex and the intercepts of the…

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Q: Suppose the coefficients of the cubic polynomial p(x) = a +bx+cx^2+dx^3 satisfy the equation:…

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Q: 2. Find a quadratic spline function having the nodes –1,0 and 1, and satisfying the table -1 |0|1 7…

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Q: find the absolute maxima and minima of the func-tions on the given domains. ƒ(x, y) = x2 + y2 on the…

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Q: ons 1-e2z (b) 3.

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Q: 1. Express the quadratic function f1x2  x2  x  6 in standard form, and sketch its graph.

A: Given: f(x)=x2−x−6

Q: 14. Determine the real values of a, b, and c for the quadratic function f(x) = ax? + bx + c, a ± 0,…

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Q: Let Q(x) = b0 + b1(x - a) + b2(x - a)2 be a quadratic approximation to ƒ(x) at x = a with these…

A: Given that, Qx=b0+b1x-a+b2x-a2            ...(1)

Q: 2. Find an equation of the form f(x) =b.a +c that has the horizontal asymptotes at y = 350,…

A: y=b is said to be a horizontal asymptote of a curve y=f(x) if as x tends to infinity (or -…

Q: (a) find the least squares approximation g(x) = a0 + a1x of the function f, and (b) use a graphing…

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Q: For the cubic polynomial function ?(?)=??3+??2+??+?,f(x)=ax3+bx2+cx+d, find ?,a, ?,b, ?,c, and ?d so…

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Q: Find a function P(x) of least possible degree, having real coefficients, with the given zeros. 03…

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Q: Find the values of constants a, b, and c so that the graph of y = (x2 + a)/(bx + c) has a local…

A: given

Q: Consider the function f(x)=xe^-7x, 0≤x≤2. Find The absoulute mininum and maximum.

A: Given data: The given function is f(x)=xe-7x. The given limits of x are [a, b]=[0, 2]. The first…

Q: a. Let Q(x) = b0 + b1(x - a) + b2(x - a)2 be a quadratic approximation to ƒ(x) at x = a with the…

A: Given:Let Q(x) = b0 + b1(x - a) + b2(x - a)2 be a quadratic approximation to ƒ(x) at x = a with the…

Q: Find the standard formf (x) = a(x – h)² + k of the quadratic function that has a vertex at (-2, 5)…

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Q: The table shows the mass of a substance decreasing over a period of time during a chemical…

A: The table is formed between the mass of the substance with respect to time. Time (s) Mass (g) 2…

Q: Determine the value of the coefficients a, b, c, d and e so that the following f(x) is a natural…

A:

Q: 15(a). Consider the quadratic function f(x)=x2- 2x-3. (i) Find the vertex and the intercepts of the…

A: (a)  To find: The vertex and intercepts of the function: Given: The quadratic function is…

Q: At z = 1, find the residue of 1/ [z(z-1)]

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Q: 1)Find the fourth degree Maclaurin polynomial for the function. f (x) = e3z

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Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3. y=f(x) 1…

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Q: Determine a quadratic function in vertex form given that it has a vertex at (3, 0) and passes…

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Q: Find the degree 3 Taylor polynomial T3(x) centered at a = 4 of the function f(x) = (-7x +32)3/2.

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Q: Find a function P(x) of least possible degree, having real coefficients, with the given zeros. 16) 3…

A: Given that 7i is a zero of the polynomial P(x). So -7i is also a zero of the polynomial.  So the…

Q: 2. Find a quadratic spline function having the nodes -1,0 and 1, and satisfying the table -1 0|1 5…

A: This question is about application of numerical method to obtain quadratic spline