4.7 Key Features of Quadratics Given Graphs

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens downwards or upwards.

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 point (0, c) in the standard form y = ax^2 + bx + c.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the x-values where the graph intersects the x-axis, found by solving the equation ax^2 + bx + c = 0.

Front

What is the significance of the y-intercept in a quadratic graph?

Back

The y-intercept indicates the value of the function when x = 0, providing insight into the function's behavior.

Front

How can you determine if the vertex is a maximum or minimum?

Back

If the coefficient 'a' is positive, the vertex is a minimum; if 'a' is negative, the vertex is a maximum.

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 formula x = -b/(2a).

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.