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Graphing Linear Equations In Standard Form

In Lesson 2.1.3, you used the method of averaging the intercepts to change the equation of a parabola

+ bx + c to the graphing form f (x) = a(x −h)

from the standard form f (x) = ax

+ k by finding the x-

intercepts and averaging them to find the x-value of the vertex. Next you substituted to find the y-value,

and then used the coordinates of the vertex for h and k.

‑

What can you say about a parabola that cannot be factored or that does not cross the x

axis? How

can you write its equation in graphing form? In a previous course you may have learned how to

complete the square for quadratics and this strategy can help you write the graphing form for a

parabola.

2-42. In this investigation you will compare two methods of changing a quadratic equation from

standard form to graphing form.

– 2x – 15 in graphing form using two methods. First,

a. Write the equation of the parabola y = x

use the method of averaging the intercepts. Then, use the method of completing the square.

Find the x‑ intercept(s), the y‑ intercept(s), and the vertex of the parabola, and sketch the

graph.

b. Write y = x

+ 8x + 10 in graphing form. Find the intercepts and vertex, and sketch the graph.

Do both strategies work for this parabola?

c. Can you use both methods to sketch y = x

+ 2x + 4. Do both strategies still work?

d. Discuss the two strategies with your team. Then respond to the following Discussion Points.

When does the method of averaging the intercepts work better?

When does the method of completing the square work better?

Which method was more efficient and why?

Graphing Linear Equations In Standard Form