Writing Quadratics Given Solutions

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 solutions of a quadratic equation called?

Back

The solutions of a quadratic equation are called roots or zeros.

Front

How do you find a quadratic equation given its roots?

Back

To find a quadratic equation given its roots r1 and r2, use the formula: (x - r1)(x - r2) = 0.

Front

What is the significance of the coefficients in a quadratic equation?

Back

The coefficients a, b, and c determine the shape and position of the parabola represented by the quadratic equation.

Front

What does it mean for a quadratic equation to have repeated roots?

Back

A quadratic equation has repeated roots when both solutions are the same, indicating that the parabola touches the x-axis at one point.

Front

Write a quadratic equation with the solutions x = 1 and x = 3.

Back

(x - 1)(x - 3) = 0 or x² - 4x + 3 = 0.

Front

Write a quadratic equation with the solutions x = -2 and x = 5.

Back

(x + 2)(x - 5) = 0 or x² + 3x - 10 = 0.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you determine the direction of a parabola from a quadratic equation?

Back

The direction of a parabola opens upwards if the coefficient a > 0 and downwards if a < 0.

Front

What is the axis of symmetry in a quadratic equation?

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).