Standard & Vertex Form of Quadratics

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you find the vertex from the standard form of a quadratic equation?

Back

To find the vertex from the standard form f(x) = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What does the 'a' value in a quadratic equation determine?

Back

The 'a' value determines the direction of the parabola (opens up if a > 0, opens down if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h, where (h, k) is the vertex.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0).

Front

What does it mean for a quadratic function to have a maximum or minimum?

Back

A maximum occurs at the vertex if the parabola opens down (a < 0), while a minimum occurs if the parabola opens up (a > 0).

Front

How can you determine the number of real roots of a quadratic equation?

Back

The number of real roots can be determined using the discriminant, D = b² - 4ac. If D > 0, there are 2 real roots; D = 0, 1 real root; D < 0, no real roots.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens up or down.