Question

Explain how to graph a quadratic in Standard Form. Why is the Vertex form much easier to graph?

A. Standard Form involves completing the square; Vertex Form directly gives vertex coordinates.
B. Standard Form has a direct y-intercept; Vertex Form lacks this feature.
C. Standard Form provides axis of symmetry; Vertex Form requires complex calculations.
D. Standard Form doesn't allow for transformations; Vertex Form is more versatile for transformations.

Answer 1

To graph a quadratic in Standard Form (y = ax² + bx + c), identify the y-intercept, find the vertex using an axis of symmetry formula, and plot symmetrical points. Vertex Form (y = a(x - h)² + k) is easier because it gives the vertex directly and shows the parabola's opening direction with no need to complete the square.

Step-by-step explanation:

To graph a quadratic equation in Standard Form, which is y = ax² + bx + c, you first identify the y-intercept by setting x to zero and solving for y. Next, you can use the axis of symmetry formula x = -b/(2a) to find the x-coordinate of the vertex. To obtain additional points, choose x-values and calculate corresponding y-values, remembering that the graph will be symmetrical about the axis of symmetry. Plot the points on a coordinate grid and draw the parabola.

The Vertex Form of a quadratic, y = a(x - h)² + k, is often considered easier to graph because it directly gives you the vertex of the parabola as (h, k). You don't need to complete the square or perform any additional calculations to find the vertex. Also, the value of a indicates whether the parabola opens upward (a > 0) or downward (a < 0) and its width. Simply plot the vertex, determine the direction the parabola opens, and select points around the vertex for a clear graph.