Math Flashcard

Front

What is the standard form of a quadratic equation?

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you factor a quadratic expression like q² + 14q + 48?

Back

To factor q² + 14q + 48, look for two numbers that multiply to 48 and add to 14. The factors are (q + 6)(q + 8).

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What does it mean for a quadratic to have complex roots?

Back

Complex roots occur when the discriminant is negative, resulting in roots that include imaginary numbers.

Front

How can you determine the vertex of a parabola represented by a quadratic equation?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.

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 x = -b/(2a).

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 do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of c in the standard form.

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

The sum of the roots is -b/a and the product of the roots is c/a, according to Vieta's formulas.