Drawing the Graph of a Quadratic Polynomial

A quadratic polynomial is a polynomial of degree 2. It is of the form ax^2 + bx + c, where a, b, and c are constants. To draw the graph of a quadratic polynomial, we need to plot points on the coordinate plane and join them with a smooth curve.

Shape of the Curve when the Coefficient of x^2 is Positive

When the coefficient of x^2 is positive, the graph of the quadratic polynomial is a parabola that opens upwards. The vertex of the parabola is the lowest point on the curve, and it lies on the axis of symmetry of the parabola. The axis of symmetry is a vertical line that passes through the vertex.

Shape of the Curve when the Coefficient of x^2 is Negative

When the coefficient of x^2 is negative, the graph of the quadratic polynomial is a parabola that opens downwards. The vertex of the parabola is the highest point on the curve, and it lies on the axis of symmetry of the parabola. The axis of symmetry is a vertical line that passes through the vertex.

Number of Zeros

The number of zeros of a quadratic polynomial is the number of x-intercepts of its graph. An x-intercept is a point where the graph of the polynomial crosses the x-axis. To find the x-intercepts, we set y = 0 in the equation of the polynomial and solve for x. If the discriminant of the quadratic equation is positive, then the polynomial has two real roots, and the graph intersects the x-axis at two points. If the discriminant is zero, then the polynomial has one real root, and the graph touches the x-axis at one point. If the discriminant is negative, then the polynomial has no real roots, and the graph does not intersect the x-axis.

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