Solve 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 does it mean to find the zeros of a quadratic function?

Back

Finding the zeros of a quadratic function means determining the values of x for which the function equals zero (f(x) = 0). These values are also known as the x-intercepts.

Front

How can you graph a quadratic function?

Back

To graph a quadratic function, plot the vertex, axis of symmetry, and x-intercepts, then draw a smooth curve (parabola) through these points.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, 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, passing through the vertex.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of a function crosses the x-axis, corresponding to the zeros of the function.

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 factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots or zeros of the function.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the coefficient 'a' in the quadratic function: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.