Final answer:
To transform a quadratic function from vertex form to intercept form, first set a = 1, then isolate the x-term, divide by a, simplify, and collect like terms to write in intercept form.
1. Find the values of a, b, and c in vertex form (y = a(x - h)² + k).
2. Set a = 1 (to simplify calculations).
3. Rearrange the equation to isolate the x-term.
4. Divide both sides by the coefficient of the x² term (a).
5. Simplify and collect like terms.
6. Write in the form of intercept form (y = mx + b).
Explanation:
Quadratic functions, represented by a parabolic curve, have a wide range of applications in various fields such as physics, engineering, and economics. The vertex form, which shows the coordinates of the lowest or highest point on the parabola, is a convenient way to write quadratic equations. However, in some cases, it may be more useful to express the function in intercept form, which shows the slope and y-intercept of the line that passes through the origin and intersects the parabola.
To transform a quadratic function from vertex form to intercept form, we follow several steps. Firstly, we set a equal to 1, which simplifies calculations and makes it easier to manipulate the equation. Next, we isolate the x-term by taking the square root of both sides and introducing a new variable b. We then divide both sides by a and simplify to obtain slope-intercept form. Finally, we collect like terms and write the equation in intercept form with both slope and y-intercept terms separated out.
Transforming quadratic functions into intercept form is essential for finding x-intercepts and y-intercepts of the function, as well as graphing it on different coordinate planes. By following these steps carefully and accurately, we can easily transform our quadratic functions into intercept form for various purposes. This process allows us to better understand and analyze quadratic equations in various real-world scenarios.