Quadratics: Solving [Part 1]

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

Identify the coefficients in the quadratic equation: 4x² - 8x - 3 = 0.

Back

a = 4, b = -8, c = -3.

Front

How do you factor the quadratic expression: 3x² - 7x - 6?

Back

The factored form is (3x + 2)(x - 3).

Front

What are the roots of the equation b² + b - 56 = 0?

Back

The roots are 7 and -8.

Front

What does it mean for a quadratic equation to have 2 real rational roots?

Back

It means the equation has two distinct solutions that are both rational numbers.

Front

How can you classify the nature of the roots of the quadratic equation y = 2x² - x - 1?

Back

The nature of the roots is 2 Real Rational Roots.

Front

What is the vertex form of a quadratic equation?

Back

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

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 the discriminant (b² - 4ac) tell us about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, two complex roots.

Front

How do you solve a quadratic equation by graphing?

Back

To solve by graphing, plot the quadratic function and identify the x-intercepts, which represent the solutions.