Solve a Quadratic 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 x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation f(x) = 0.

Front

How do you find the vertex of a parabola?

Back

The vertex of a parabola given by the equation f(x) = ax² + bx + c can be found using the formula x = -b/(2a).

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 equation x = -b/(2a).

Front

What does it mean if a quadratic has no real solutions?

Back

If a quadratic has no real solutions, it means the parabola does not intersect the x-axis, which occurs when the discriminant (b² - 4ac) is less than zero.

Front

What is the discriminant in a quadratic equation?

Back

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

Front

What are the possible values of the discriminant and their meanings?

Back

If the discriminant is positive, there are two real solutions; if zero, there is one real solution; if negative, there are no real solutions.

Front

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined by evaluating the discriminant: positive (two solutions), zero (one solution), negative (no solutions).

Front

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

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.