Solving Quadratic Functions

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They are also known as roots or x-intercepts.

Front

How do you solve the quadratic equation 4x² + 2x - 6 = 0?

Back

You can solve it using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. For this equation, a = 4, b = 2, c = -6, leading to solutions x = 1 and x = -1.5.

Front

True or False: The solution, root, x-intercept, and zero of a quadratic function are all the same thing.

Back

True. They all refer to the points where the quadratic function intersects the x-axis.

Front

What does it mean if a quadratic equation has one solution?

Back

It means the graph of the quadratic touches the x-axis at exactly one point, indicating a repeated root.

Front

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

Back

You can determine the number of solutions by calculating the discriminant (b² - 4ac). If it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

Front

What are the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have two solutions, one solution, or no real solutions.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

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

Back

For a quadratic in the form y = ax² + 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 is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.