Quadratic Key Features ALL FORMS

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation. It is represented as the point (h, k) in the vertex form of a quadratic equation y = a(x - h)² + k.

Front

What are the roots of a quadratic function?

Back

The roots (or zeros) of a quadratic function are the values of x where the function equals zero. They can be found by factoring, using the quadratic formula, or graphing.

Front

True or false: The solution, root, x-intercept, and zero of a quadratic function are all the same thing.

Back

True. They all refer to the points where the graph of the function intersects the x-axis.

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

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 the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the equation.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation ax² + bx + c.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the significance of the 'k' value in vertex form?

Back

The 'k' value represents the y-coordinate of the vertex and indicates the vertical shift of the parabola.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the 'a' value in the quadratic equation is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.