Solving Quadratics

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero. They are also known as the roots of the function.

Front

What is the relationship between the zeros and the graph of a quadratic function?

Back

The zeros of a quadratic function are the x-intercepts of its graph, where the graph crosses the x-axis.

Front

Define the term 'roots' in the context of quadratic equations.

Back

Roots are the solutions to the equation when set to zero, representing the x-values where the graph intersects the x-axis.

Front

What is the vertex of a quadratic function?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic in standard form y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a).

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 does it mean if a quadratic equation has no real solutions?

Back

If a quadratic equation has no real solutions, it means the graph does not intersect the x-axis, indicating that the discriminant (b^2 - 4ac) is less than zero.

Front

How can you determine the number of real solutions of a quadratic equation?

Back

The number of real solutions can be determined by calculating the discriminant (b^2 - 4ac): if it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

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.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form. 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for x.