A quadratic equation in standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
What is the quadratic formula used for?
The quadratic formula is used to find the solutions (roots) of a quadratic equation.
State the quadratic formula.
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).
What does the discriminant in a quadratic equation tell us?
The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation.
What are the possible outcomes for the roots based on the discriminant?
If b² - 4ac > 0, there are two real and distinct roots; if b² - 4ac = 0, there is one real root (repeating); if b² - 4ac < 0, there are no real roots, only complex roots.
How many solutions does a quadratic equation have?
A quadratic equation can have two, one, or no real solutions.
What is factoring and how is it related to quadratic equations?
Factoring is a method used to solve quadratic equations by expressing the equation as a product of linear factors.
Give an example of a simple quadratic equation.
An example of a simple quadratic equation is x² - 5x + 6 = 0.
What do we need to do if a quadratic equation cannot be factored easily?
If a quadratic equation cannot be factored easily, we can use the quadratic formula or complete the square method to solve it.
Explain completing the square method for solving a quadratic equation.
Completing the square involves transforming the quadratic equation into a perfect square trinomial, making it easier to solve by taking square roots.
What does 'quadratic' mean?
The term 'quadratic' comes from 'quad', meaning square, because the variable is squared (x²).
Why must 'a' not be zero in a quadratic equation?
If 'a' were zero, the equation would no longer be quadratic; it would become linear.
What is the vertex form of a quadratic equation?
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
What graph shape does a quadratic equation form?
The graph of a quadratic equation forms a parabola.
What determines the direction of a parabola (upward or downward) in a quadratic graph?
The sign of 'a' determines the direction: if 'a' is positive, the parabola opens upwards; if negative, it opens downwards.