Solving Quadratic Functions 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 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 roots of a quadratic function?

Back

The roots of a quadratic function are the values of x for which the function equals zero, i.e., the points where the graph intersects the x-axis.

Front

How can you determine the number of roots of a quadratic function from its graph?

Back

The number of roots can be determined by the number of times the parabola intersects the x-axis: 0 intersections means no real roots, 1 intersection means one real root, and 2 intersections mean two real roots.

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

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.

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, and it passes through the vertex. Its equation is x = -b/(2a).

Front

What is the discriminant in the context of quadratic functions?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b² - 4ac. It determines the nature of the roots: 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

How can you use the discriminant to determine the number of solutions?

Back

By calculating the discriminant (D = b² - 4ac), you can determine the number of solutions: D > 0 indicates two solutions, D = 0 indicates one solution, and D < 0 indicates no solutions.

Front

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

Back

The y-intercept is the point where the graph intersects the y-axis, which occurs when x = 0. It can be found by evaluating the function at x = 0, giving the value c in the standard form f(x) = ax² + bx + c.