Solving Quadratic Equations

When does a quadratic equation have two distinct real solutions?

• A quadratic equation has two distinct real solutions when the discriminant (D) is greater than zero (D > 0).

• A quadratic equation has two distinct real solutions when the discriminant (D) is equal to zero (D = 0).

• A quadratic equation has two distinct real solutions when the coefficients are all positive.

• A quadratic equation has two distinct real solutions when the roots are complex.

What is the quadratic formula?

• @@x=rac{-b ext{±} ext{√}(b^2-4ac)}{2a}@@

• @@x=rac{-b ext{±} ext{√}(b^2+4ac)}{2a}@@

• @@x=rac{-b ext{±} ext{√}(b^2-2ac)}{2a}@@

• @@x=rac{-b}{2a}@@

What is the significance of the roots of a quadratic equation?

• They represent the maximum value of the quadratic function.

• They are the x-values where the graph intersects the x-axis, representing the solutions to the equation.

• They indicate the direction of the parabola's opening.

• They determine the y-intercept of the quadratic function.

What is the discriminant in a quadratic equation?

• The part of the quadratic formula that determines the number of solutions, given by D = b² - 4ac.

• The coefficient of the linear term in the quadratic equation.

• The constant term in the quadratic equation that affects the graph's position.

• The value that represents the maximum point of the parabola.

How do you solve a quadratic equation?

• Graphing

• Completing the square

• Quadratic Formula

• Adding and Subtracting

What are the possible types of solutions for a quadratic equation?

• Two real solutions, one real solution (a repeated root), or no real solutions.

• Only two real solutions.

• Only one real solution.

• At least one real solution.

What is completing the square in relation to quadratic equations?

• A method to factor quadratic equations into linear terms.

• A technique to find the roots of a quadratic equation using the quadratic formula.

• A method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q.

• A process to convert a quadratic equation into a polynomial of degree one.

What is vertex form of a quadratic function?

• f(x) = a(x - h)^2 + k

• f(x) = ax^2 + bx + c

• f(x) = a(x + h)^2 - k

• f(x) = a(x - h)^2 - k

What is a quadratic equation?

• A polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

• A linear equation of the form ax + b = 0, where a and b are constants.

• A polynomial equation of the form ax³ + bx² + cx + d = 0, where a, b, c, and d are constants.

• An equation that represents a straight line on a graph.

When does a quadratic equation have one real solution?

• When the discriminant (D) is greater than zero (D > 0).

• When the discriminant (D) is less than zero (D < 0).

• When the discriminant (D) is equal to zero (D = 0).

• When the quadratic equation is in vertex form.