Solving Quadratics

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 is the quadratic formula?

Back

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

Front

What does it mean for a quadratic equation to have no real solutions?

Back

A quadratic equation has no real solutions when the discriminant (b² - 4ac) is less than 0, indicating that the parabola does not intersect the x-axis.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, you need to express it in the form (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, and it determines the nature of the roots.

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x.

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What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, found at the coordinates (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 solve a quadratic equation by taking square roots?

Back

To solve by taking square roots, isolate the x² term, then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the x-values where the function equals zero, also known as the roots or solutions of the equation.