Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to 'complete the square'?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

Front

What is the formula for completing the square for the equation x² + bx?

Back

The formula is x² + bx = (x + b/2)² - (b/2)².

Front

How do you solve a quadratic equation by taking the square root?

Back

To solve by taking the square root, isolate x² on one side of the equation and then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b/(2a) and k is the value of the quadratic function at h.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

How can you determine the number of solutions from a graph of a quadratic function?

Back

The number of solutions corresponds to the number of times the graph intersects the x-axis: two intersections mean two solutions, one intersection means one solution, and no intersections mean no solutions.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the factored form of a quadratic equation?

Back

The factored form is expressed as a(x - r₁)(x - r₂) where r₁ and r₂ are the roots of the equation.