Factoring/Solving Quadratics from a graph

Front

What is a quadratic equation?

Back

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

Front

What are the solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called roots or zeros.

Front

How can you find the roots of a quadratic equation graphically?

Back

The roots of a quadratic equation can be found graphically by identifying the x-intercepts of the parabola represented by the equation.

Front

What is the factored form of a quadratic equation?

Back

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

Front

What does it mean for a quadratic to have real solutions?

Back

A quadratic has real solutions if its graph intersects the x-axis at one or two points, indicating that the discriminant (b^2 - 4ac) is greater than or equal to zero.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

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 formula x = -b/(2a).

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 positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

How do you convert a quadratic equation 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 quadratic formula?

Back

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