Quadratics in Standard & Vertex Form

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is given by the equation y = ax^2 + bx + c, where a, b, and c are constants.

Front

What do the coefficients A, B, and C represent in the quadratic equation y = Ax^2 + Bx + C?

Back

In the quadratic equation y = Ax^2 + Bx + C, A represents the coefficient of x^2, B represents the coefficient of x, and C represents the constant term.

Front

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

Back

A quadratic function opens upwards if the coefficient A (in y = Ax^2 + Bx + C) is positive, and it opens downwards if A is negative.

Front

What is the vertex of a quadratic function, and how is it found?

Back

The vertex of a quadratic function in standard form can be found using the formula (-B/(2A), f(-B/(2A))), where A and B are the coefficients from the standard form.

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry for a quadratic function in standard form y = Ax^2 + Bx + C is given by the line x = -B/(2A).

Front

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

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the value of C in the standard form y = Ax^2 + Bx + C.

Front

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

Back

The discriminant (D = B^2 - 4AC) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is vertex form of a quadratic function?

Back

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

Front

How can you convert a quadratic function from standard form to vertex form?

Back

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

Front

What is the relationship between the vertex and the maximum or minimum value of a quadratic function?

Back

The vertex of a quadratic function represents the maximum value if the parabola opens downwards (A < 0) and the minimum value if it opens upwards (A > 0).