Factoring/Solving Quadratics from a graph

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as (x - p)(x - q), where p and q are the roots of the equation.

Front

How do you find the solutions of a quadratic equation from its graph?

Back

The solutions of a quadratic equation can be found by identifying the x-intercepts (roots) of the parabola on the graph.

Front

What does it mean if a quadratic has 'no solution'?

Back

A quadratic has 'no solution' when the graph does not intersect the x-axis, indicating that there are no real roots.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts of a parabola are the points where the graph crosses the x-axis, corresponding to the solutions of the quadratic equation.

Front

How can you determine the factored form of a quadratic from its roots?

Back

If the roots of a quadratic are known, the factored form can be written as (x - root1)(x - root2).

Front

What is the vertex of a parabola?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by ax^2 + bx + c = 0, where a, b, and c are constants.

Front

How do you convert a quadratic from standard form to factored form?

Back

To convert from standard form to factored form, you can use factoring techniques such as grouping, the quadratic formula, or completing the square.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What does it mean for a quadratic to be 'irreducible'?

Back

A quadratic is 'irreducible' if it cannot be factored over the set of real numbers, typically when the discriminant is negative.