Solving Quadratics by graphing

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + 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 ax² + bx + c = 0.

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 are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph crosses the x-axis, also known as the zeros or roots of the function.

Front

How can you determine the number of solutions a quadratic equation has?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac). If D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

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 upwards or downwards.

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

What is the significance of the vertex in solving quadratic equations?

Back

The vertex provides the maximum or minimum value of the quadratic function, which can help in determining the range of the function.

Front

What does it mean for a quadratic function to have no real solutions?

Back

It means that the graph of the function does not intersect the x-axis, indicating that the discriminant is negative.

Front

What is a maximum point in the context of a quadratic function?

Back

A maximum point is the highest point on the graph of a quadratic function that opens downwards.