Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant determines the nature of the roots: if > 0, there are 2 real solutions; if = 0, there is 1 real solution; if < 0, there are no real solutions.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is the vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

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

Back

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

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 is a parabola?

Back

A parabola is a U-shaped graph that represents a quadratic function, defined by a quadratic equation.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means the graph of the quadratic does not intersect the x-axis, indicating that the discriminant is less than zero.

Front

Solve using the quadratic formula: 2x² + 2x - 12 = 0

Back

x = 2, -3.

Front

Solve using the quadratic formula: 4x² + 4x + 1 = 0

Back

x = -½.

Front

If a quadratic equation has one real solution, what does that indicate about its graph?

Back

The graph touches the x-axis at exactly one point, indicating that the vertex lies on the x-axis.