Standard to Vertex Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by the formula: 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 given by the formula: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

To convert from standard form (ax² + bx + c) to vertex form (a(x - h)² + k), complete the square on the quadratic expression.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic expression in the form (x - p)² - q, where p and q are constants, by adding and subtracting the square of half the coefficient of x.

Front

What is the vertex of the parabola represented by the equation y = (x - 3)² - 5?

Back

The vertex of the parabola is the point (3, -5).

Front

How can you identify the direction of a parabola from its vertex form?

Back

The direction of a parabola can be identified from the coefficient 'a' in the vertex form: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What does the term 'axis of symmetry' refer to in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it can be found using the formula x = h, where (h, k) is the vertex.

Front

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

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you find the y-intercept of a quadratic function in standard form?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of c in the standard form ax² + bx + c.

Front

What is the relationship between the coefficients of a quadratic equation and the roots of the equation?

Back

The roots of the quadratic equation ax² + bx + c = 0 can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).