8) 4 Complete the square to transform the quadratic equation into the form (x - p)2-q....
40 Use the method of completing the square to transform the quadratic equation into the equation form (x -p2-q. ?9 + 12x-6x2 =0 A) (x-1)2??0.5 B) 12- -1.5 C) D) (1)2-1.5 (x-1)2-0.5
1(a) Find the square roots of the complex number z -3 + j4, expressing your answer in the form a + jb. Hence find the roots for the quadratic equation: x2-x(1- 0 giving your answer in the form p+ q where p is a real number and q is a complex number. I7 marks] (b) Express: 3 + in the form ω-reje (r> 0, 0 which o is real and positive. θ < 2π). Hence find the smallest value of...
Solving a quadratic equation by completing the square: Exact... Solve the quadratic equation by completing the square. x² + 12x+33=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form: DIE 0 00 (x+D- (x-0²=0 Solution: Check Explanation F2 esc
4. Identify and sketch the conic sections and quadratic surfaces of equation Q(x) - 1, when Q(x) is a quadratic form defined by one of the following matrices (b) 1 2 1 (c)0 0 0 3 0 -1 2 4 -3 (d)4 1 3 4. Identify and sketch the conic sections and quadratic surfaces of equation Q(x) - 1, when Q(x) is a quadratic form defined by one of the following matrices (b) 1 2 1 (c)0 0 0 3...
7. Solve the quadratic inequalities: P(x)-x2 +3x+ 10:P(x) s 0 a. Find the constant variation and write the related variation equation: a. C varies directly with R and inversely with the squared of s. 8. C 21 when R-17 and s-1.5 J varies directly with P and inversely with square root of Q. J-19 when P-4 and Q-25 b. -THE END
Solve the quadratic equation by completing the square. x? +18x+66=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas. Form: . 0/0 00... o (v + D² = 0 o (v - D’= 0 X 5 ? Solution: x= -9 + √15, -9 - Vis
Consider the quadratic form Q(x) xỈ + x2 + x + 4X1X2 + 4x2x3 + 4x3x1. (a) Find the real symmetric matrix A so that Q(X) = XTAX. (b) Find an orthogonal matrix Q so that the change of variables x = Qy transforms the quadratic for Q(x) into one with no cross-product terms, that is, diagonalize the quadratic form (x). Give the transformed quadratic form. (c) Find a vector x of length 1 at which Q(x) is maximized. (d)...
Investigation 4: Quadratic Equations The quadratic equation is typically written in the form and has the solution 2a In this Investigation, we will look at a number of equations, rearrange them to be in this form, and identify which variables correspond to a, b, c, & x in the definition above. Activity 1-8: For each of the expressions, do the following Is it absolutely necessa ry to use the quadratic equation to solve the expression? . egardless of whether you...
3. List the vertex form of the quadratic function and state all relevant information. 4. Convert the quadratic form f(x) +3-4 into standard form (le. multiply t out). Then check your solution to example 2. 5. Continuing with example 2, read the questions and solutions. Paying particular attention to part d. How can we find the axis of symmetry (aka the x-value of the vertex)? 6. (Note: we will not be covering 'completing the square' in this class, but feel...
(2) Express the quadratic form Q=x; -x} - 4x,x2 + 4xzxz in terms of diagonal quadtratic form.Use X(X1, X2, X3)=PY(y1,92,93) 121 Tannster.T.D-D alhym2) - (2. Ihim