quadratic formula

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 ax² + bx + c = 0.

Front

In the quadratic equation y = ax² + bx + c, what does 'a' represent?

Back

'a' represents the coefficient of the x² term, which determines the direction and width of the parabola.

Front

In the quadratic equation y = ax² + bx + c, what does 'b' represent?

Back

'b' represents the coefficient of the x term, which affects the position of the vertex of the parabola.

Front

In the quadratic equation y = ax² + bx + c, what does 'c' represent?

Back

'c' represents the constant term, which is the y-intercept of the parabola.

Front

What is the significance of the discriminant (b² - 4ac) in a quadratic equation?

Back

The discriminant determines the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert, complete the square on the quadratic equation to express it in the form y = a(x - h)² + k, where (h, k) is the vertex.

Front

What are the x-intercepts of a quadratic equation?

Back

The x-intercepts are the points where the graph of the quadratic equation crosses the x-axis, found by setting y = 0 and solving for x.

Front

How can you find the vertex of a parabola given the quadratic equation in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h), the value of the function at x = h.

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 the equation x = -b/(2a).

Front

What does it mean for a quadratic equation to be in standard form?

Back

A quadratic equation is in standard form when it is expressed as y = ax² + bx + c, where a, b, and c are constants.