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 the graph of a quadratic equation look like?

Back

The graph of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens downwards or upwards.

Front

How do you determine if a parabola has a maximum or minimum?

Back

If the coefficient 'a' is positive, the parabola opens upwards and has a minimum. If 'a' is negative, it opens downwards and has a maximum.

Front

What is the line of symmetry in a quadratic equation?

Back

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

Front

How do you find the x-intercepts of a quadratic equation?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x, often using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the factored form of a quadratic equation?

Back

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

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert to vertex form, use the method of completing the square: y = a(x - h)² + k, where (h, k) is the vertex.