(Alg.2) 4.3 (Flashcard) Quadratics in Vertex and Intercept form.

Front

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

Back

The vertex of a quadratic function in vertex form, given by the equation f(x) = a(x - h)^2 + k, is the point (h, k).

Front

How do you determine if a parabola opens up or down?

Back

A parabola opens up if the coefficient 'a' in the vertex form f(x) = a(x - h)^2 + k is positive. It opens down if 'a' is negative.

Front

What is the intercept form of a quadratic function?

Back

The intercept form of a quadratic function is written as y = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How do you find the vertex from the intercept form?

Back

To find the vertex from the intercept form y = a(x - p)(x - q), calculate the x-coordinate as (p + q)/2 and substitute it back into the equation to find the y-coordinate.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How can you convert from vertex form to standard form?

Back

To convert from vertex form f(x) = a(x - h)^2 + k to standard form, expand the equation: f(x) = a(x^2 - 2hx + h^2) + k.

Front

What is the significance of the x-intercepts in a quadratic function?

Back

The x-intercepts (roots) of a quadratic function are the points where the graph intersects the x-axis, indicating the values of x for which f(x) = 0.

Front

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

Back

To find the y-intercept of a quadratic function, substitute x = 0 into the function and solve for f(0).

Front

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

Back

The 'a' value in a quadratic function determines the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function in vertex form f(x) = a(x - h)^2 + k is the vertical line x = h.