Polynomial/Quadratics Review

Front

What does a discriminant of zero indicate about the solutions of a quadratic equation?

Back

It indicates that there is 1 real solution.

Front

What are the factors and solutions of the equation x² + 2x - 3 = 0?

Back

Factors: (x - 1)(x + 3); Solutions: x = 1, x = -3.

Front

Solve the equation by factoring: x² + 13x + 40 = 0.

Back

Solutions: x = -8, x = -5.

Front

What is the discriminant of the quadratic equation 6x² - 2x - 3 = 0?

Back

The discriminant is 76.

Front

Use the quadratic formula to find the solutions for y = -x² - 5x + 12.

Back

Solutions: x = 2, x = -6.

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.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c.

Front

What is the vertex of a parabola represented by a quadratic function?

Back

The vertex is the highest or lowest point of the 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 images, given by the formula x = -b/(2a).

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x that make the equation equal to zero, also known as solutions.