Solving Quadratics

Front

What are the zeros of a quadratic equation?

Back

The zeros of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, the quadratic formula, or graphing.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the zeros. Then, set each factor equal to zero and solve for x.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are two complex roots.

Front

What is the square root property in solving quadratics?

Back

The square root property states that if x² = k, then x = ±√k. This can be used to solve equations where the variable is squared.

Front

How do you complete the square to solve a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the x² and x terms, then add (b/2)² to both sides to form a perfect square trinomial.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form (ax² + bx + c) is given by the formula x = -b/(2a).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, find the vertex, axis of symmetry, and zeros. Plot these points and draw a smooth curve through them.