Writing Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

What does the 'a' in a quadratic function represent?

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

How do you convert from vertex form to standard form?

Back

To convert from vertex form y = a(x-h)² + k to standard form, expand the equation and simplify to the form y = ax² + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, located at the point (h, k) in the vertex form y = a(x-h)² + k.

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 = h, where (h, k) is the vertex.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set y = 0 and solve the quadratic equation ax² + bx + c = 0 using factoring, completing the square, or the 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.

Front

What is the vertex form of a quadratic function?

Back

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