Quadratic Equations

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 values of a, b, and c in the equation 3x² - 8x + 15 = 0?

Back

a = 3, b = -8, c = 15.

Front

How do you find the vertex of a parabola given the equation y = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the vertex of the parabola represented by the equation y = -2x² + 4x + 3?

Back

The vertex is (1, 5).

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

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

How do you convert from standard form to vertex form?

Back

You can complete the square to rewrite the equation in vertex form.

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, no real roots.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).