Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the zeros of a quadratic equation?

Back

The zeros (or roots) of a quadratic equation are the values of x that make the equation equal to zero. They represent the x-intercepts of the parabola.

Front

How can you determine the number of zeros a quadratic equation has?

Back

The number of zeros can be determined using the discriminant (D = b² - 4ac). If D > 0, there are 2 distinct zeros; D = 0 means 1 zero; D < 0 indicates no real zeros.

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 y = ax² + bx + c.

Front

What is the intercept form of a quadratic equation?

Back

The intercept form of a quadratic equation is f(x) = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the equation using these numbers.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

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 of the equation does not intersect the x-axis, which occurs when the discriminant is negative.

Front

What is the axis of symmetry in a parabola?

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).