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Let f(x) = ax + bx+c -4 Choose appropriate values of a, b, and c such...
The graph of a function of the form f(x)=ax^2 + bx + c for different values of a, b, and c is given. For the function, find the following. (a) Determine if the discriminant is positive, negative, or zero. (b) Determine if there are 0, 1, or 2 real solutions to f(x)=0. (c) Solve the equation f(x)=0.
Let f(x) = ax^2 +bx +c be a quadratic whose coefficients a, b, c are rational. Prove that if f(x) has one rational root, then the other root is also rational.
12) Let f(A) = x + 1 xxo 0 x=0 (ax+ 2 x>0 a) Find lim f(x). X-70 b) Find lim F(x). X70 c) Find lim f(x). 13) Let f(x) = x - x .O 12.1 x 0 a) Find lim f(x). 6) Find
hint: H3. Let W1 = {ax? + bx² + 25x + a : a, b e R}. (a) Prove that W is a subspace of P3(R). (b) Find a basis for W. (c) Find all pairs (a,b) of real numbers for which the subspace W2 = Span {x} + ax + 1, 3x + 1, x + x} satisfies dim(W. + W2) = 3 and dim(Win W2) = 1. H3. (a) Use Theorem 1.8.1. (b) Let p(x) = ax +...
(1 point) Find a polynomial of the form f(x) = ax’ + bx² +cx +d such that f(0) = -3, f(-2) = 5, f(-3) = 2, and f(4) = 5. Answer: f(x) =
How : For what values of a, b is gu)-ax+bx, x 23a-b, ocX<2 X72 3X-5 continhows at every X How Apply tépetal Rule liult x-2 X2 x?_u How : For what values of a, b is gu)-ax+bx, x 23a-b, ocX<2 X72 3X-5 continhows at every X How Use the Implicit differentiation to find dy
Find an equation of the form y=ax'+bx+c that defines the parabola through the three noncollinear points given. (0,6), (5, 46),(-2, 4) The equation of the parabola is y-
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
show work please Quir 8(10 points) standard form of quadratic function: f(x)-ax+bx + c Factored fom: Cx)-acx-rx-a) uadratic formula Solive the following equations using any method 2 x-9x+18- 3. 50x2-128 4 2x2-11x+9 0 6. -x2 + 3x + 4 = 0 2x2-2x-1=0
Question 2. Let f(x) = azt for a, b, c, d e C, ad - bc +0. [2]a) Show lim + f() = oo if c = 0. [2]b) With c#0, show lim + f() = ? and lim,--4f(x) = 0.