Solve Quadratics by Graphing Practice

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean for a quadratic function to have two solutions?

Back

A quadratic function has two solutions when its graph intersects the x-axis at two distinct points.

Front

What does it mean for a quadratic function to have one solution?

Back

A quadratic function has one solution when its graph touches the x-axis at exactly one point, known as a double root.

Front

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

Back

A quadratic function has no real solutions when its graph does not intersect the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function 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 standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.