Solving Quadratic Equations

Front

What is a quadratic equation?

Back

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

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant indicates the nature of the roots of a quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, found at the point (h, k) in the vertex form y = a(x - h)² + k.

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

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex, calculated using the vertex formula y = a(h)² + k.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the significance of the leading coefficient (a) in a quadratic equation?

Back

The leading coefficient determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

How do you determine the roots of a quadratic equation using the quadratic formula?

Back

Substitute the values of a, b, and c into the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) to find the roots.