What are the coordinates of the vertex for the quadratic function y = (x - 3)^2 + 4?
Quadratic Functions Complex Numbers
Question · Easy
Factor it
Short
Which of the following is the complete factored form of x^2 - 9x + 20?
What is the simplified form of sqrt(-36) in terms of the imaginary unit i?
What is the equation of the axis of symmetry for the parabola f(x) = 2(x + 5)^2 - 7?
Simplify the complex number expression: (4 + 3i) + (2 - 5i).
What is the value of the discriminant for the quadratic equation x^2 - 6x + 9 = 0?
What is the simplified value of i^14?
What are all solutions to the quadratic equation x^2 - 16 = 0?
What is the y-intercept of the quadratic function y = 3x^2 - 4x + 7?
Convert the quadratic function y = x^2 - 8x + 11 into vertex form by completing the square.
Question · Medium
What are the solutions to the quadratic equation 2x^2 + 5x - 3 = 0?
What are the complex solutions to the quadratic equation x^2 - 4x + 13 = 0?
Multiply the complex numbers and express in standard a + bi form: (3 + 2i)(1 - 4i).
Which expression represents the complete factorization of 3x^2 + 10x + 8?
The height h(t) in feet of a projectile after t seconds is given by h(t) = -16t^2 + 64t + 5. What is the maximum height reached by the projectile?
Express the complex quotient 5 / (2 + i) in standard a + bi form.
Calculate the discriminant of 3x^2 - 2x + 4 = 0 and state the nature of its roots.
Solve x^2 + 6x + 25 = 0 by completing the square.
What are all real values of x that satisfy (2x - 3)^2 = 49?
Which quadratic equation in standard form has roots x = 3 and x = -7?
Expand and simplify (5 - 2i)^2 in standard form a + bi.
Find the vertex of the quadratic function y = -2x^2 + 12x - 10.
Express sqrt(-48) in simplified radical form with the imaginary unit i.
What are the solutions to x^2 - 10x + 34 = 0?
What are the intersection points of the parabola y = x^2 - 4x + 3 and the line y = 2x - 5?
Question · Hard
Simplify the complex number fraction (3 + i) / (2 - 3i) to standard a + bi form.
Find the quadratic function in vertex form y = a(x - h)^2 + k that has vertex (2, 7) and passes through the point (5, -2).
What are the complex solutions to the quadratic equation 4x^2 - 12x + 25 = 0?
What are all four real solutions to the equation x^4 - 13x^2 + 36 = 0?
Evaluate the complex power (1 + i)^4.
Add the polynomials: (3x^2 + 5x - 4) + (2x^2 - 8x + 9).
Polynomials Expressions
Subtract the polynomials: (7x^2 - 3x + 2) - (4x^2 + 5x - 6).
Simplify using exponent rules: (x^4)^(3/2).
Evaluate the expression 64^(2/3).
Simplify the radical expression sqrt(75x^4).
Multiply the binomials: (2x - 3)(x + 4).
Simplify the expression (x^(-1/2) * y^(3/4)) / (x^(3/2) * y^(-1/4)) and express with positive exponents.
Multiply the polynomial by the binomial: (x^2 - 3x + 4)(2x - 5).
Simplify the radical expression cube root of 54x^7 y^5.
Rationalize the denominator of 6 / (sqrt(5) - 1).
Solve the radical equation sqrt(3x + 1) = 5.
Simplify the expression (27x^9 y^(-6))^(2/3).
Expand the cubic binomial (2x - 3y)^3.
Solve the radical equation sqrt(2x + 15) = x for all valid real solutions.
Simplify the expression by combining like radicals: sqrt(18) + sqrt(50) - sqrt(32).
Evaluate (16)^(-3/4).
Solve the radical equation sqrt(x + 7) - sqrt(x) = 1.
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