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Magazine Problem 25
Graph the system of quadratic inequalities. (See Example 3.) \(y \geq 2 x^2+x-5\) \(y<-x^2+5 x+10\)
Problem 29
Solve the system by elimination. \(-3 x^2+y=-18 x+29\) \(-3 x^2-y=18 x-25\)
Problem 30
Add or subtract. Write the answer in standard form. \(-3+(8+2 i)+7 i\)
Problem 36
Find a possible pair of integer values for \(a\) and \(c\) so that the quadratic equation has the given solution(s). Then write the equation. \(a x^2+6 x+c=0\); two real solutions
Problem 38
Multiply. Write the answer in standard form. \(2 i(7-i)\)
Problem 39
Solve the system using any method. Explain your choice of method. \(-2 x+10+y=\frac{1}{3} x^2\) \(y=10\)
Problem 39
Can you solve an equation by completing the square when the equation has two imaginary solutions? Explain.
Problem 39
Find a possible pair of integer values for \(a\) and \(c\) so that the quadratic equation has the given solution(s). Then write the equation. \(a x^2+10 x=c ;\) one real solution
Problem 43
Determine whether you would use factoring, square roots, or completing the square to solve the equation. Explain your reasoning. Then solve the equation. \((x+4)^2=16\)
Problem 43
Multiply. Write the answer in standard form. $$ (3-6 i)^2 $$ 44
