Continuing to Payment will take you to apayment page

Purchasing
SparkNotes PLUS
for a group?

Get Annual Plans at a discount when you buy 2 or more!

Price

$24.99$18.74/subscription + tax

Subtotal $37.48 + tax

Save 25%
on 2-49 accounts

Save 30%
on 50-99 accounts

Want 100 or more?
Contact us
for a customized plan.

Continuing to Payment will take you to apayment page

Your Plan

Payment Details

Payment Details

Payment Summary

SparkNotes Plus

You'll be billed after your free trial ends.

7-Day Free Trial

Not Applicable

Renews June 24, 2024June 17, 2024

Discounts (applied to next billing)

DUE NOW

US $0.00

SNPLUSROCKS20 | 20%Discount

This is not a valid promo code.

Discount Code(one code per order)

SparkNotes PLUS
Annual Plan - Group Discount

Qty: 00

SubtotalUS $0,000.00

Discount (00% off)
-US $000.00

TaxUS $XX.XX

DUE NOWUS $1,049.58

SparkNotes Plus subscription is $4.99/month or $24.99/year as selected above. The free trial period is the first 7 days of your subscription. TO CANCEL YOUR SUBSCRIPTION AND AVOID BEING CHARGED, YOU MUST CANCEL BEFORE THE END OF THE FREE TRIAL PERIOD. You may cancel your subscription on your Subscription and Billing page or contact Customer Support at custserv@bn.com. Your subscription will continue automatically once the free trial period is over. Free trial is available to new customers only.

Choose Your Plan

Your Free Trial Starts Now!

For the next 7 days, you'll have access to awesome PLUS stuff like AP English test prep, No Fear Shakespeare translations and audio, a note-taking tool, personalized dashboard, & much more!

Thank You!

You’ve successfully purchased a group discount. Your group members can use the joining link below to redeem their group membership. You'll also receive an email with the link.

No URL

Copy

Members will be prompted to log in or create an account to redeem their group membership.

Thanks for creating a SparkNotes account! Continue to start your free trial.

We're sorry, we could not create your account. SparkNotes PLUS is not available in your country. See what countries we’re in.

There was an error creating your account. Please check your payment details and try again.

Please wait while we process your payment

Your PLUS subscription has expired

We’d love to have you back! Renew your subscription to regain access to all of our exclusive, ad-free study tools.

Renew your subscription to regain access to all of our exclusive, ad-free study tools.

We have already discovered how to graph linear functions. But what does the graph of y = x^{2} look like? To find the answer, make a data table:

And graph the points, connecting them with a smooth curve:
The shape of this graph is a parabola.

Note that the parabola does not have a constant slope. In fact, as x increases by 1, starting with x = 0, y increases by 1, 3, 5, 7,…. As x decreases by 1, starting with x = 0, y again increases by 1, 3, 5, 7,….

Graphing y = (x - h)^{2} + k

In the graph of y = x^{2}, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.

We can graph a parabola with a different vertex. Observe the graph of y = x^{2} + 3:

The graph is shifted up 3 units from the graph of y = x^{2}, and the vertex is (0, 3).

Observe the graph of y = x^{2} - 3:
The graph is shifted down 3 units from the graph of y = x^{2}, and the vertex is (0, - 3).

We can also shift the vertex left and right. Observe the graph of y = (x + 3)^{2}:

The graph is shifted left3 units from the graph of y = x^{2}, and the vertex is (- 3, 0).

Observe the graph of y = (x - 3)^{2}:
The graph is shifted to the right3 units from the graph of y = x^{2}, and the vertex is (3, 0).

In general, the vertex of the graph of y = (x - h)^{2} + k is (h, k). For example, the vertex of y = (x - 2)^{2} + 1 is (2, 1):