This question has 3 parts (a, b and c). A parabola has equation y = 2(x + 6)2 − 2.a. Expand and simplify to write the equation in the form y = ax2 + bx + c.b. Factor your equation from part a).c. Do the three equations represent the same parabola? Justify your response by making graphs. Attach image of the graph.
Question
This question has 3 parts (a, b and c). A parabola has equation y = 2(x + 6)2 − 2.a. Expand and simplify to write the equation in the form y = ax2 + bx + c.b. Factor your equation from part a).c. Do the three equations represent the same parabola? Justify your response by making graphs. Attach image of the graph.
Solution
a. To expand and simplify the equation y = 2(x + 6)² - 2, we first expand the term (x + 6)². This gives us x² + 12x + 36. We then multiply each term by 2, giving us 2x² + 24x + 72. Finally, we subtract 2 from the constant term to get 2x² + 24x + 70. So, the equation in the form y = ax² + bx + c is y = 2x² + 24x + 70.
b. To factor the equation y = 2x² + 24x + 70, we first factor out a 2 from each term, giving us y = 2(x² + 12x + 35). Then, we factor the quadratic x² + 12x + 35 into (x + 5)(x + 7). So, the factored form of the equation is y = 2(x + 5)(x + 7).
c. The three equations y = 2(x + 6)² - 2, y = 2x² + 24x + 70, and y = 2(x + 5)(x + 7) do represent the same parabola. This is because they are equivalent forms of the same equation. The first equation is in vertex form, the second is in standard form, and the third is in factored form. All three forms provide different information about the parabola, but they all describe the same parabola.
As a text-based AI, I'm unable to create and attach images. However, you can easily graph these equations using a graphing calculator or an online graphing tool. You will see that all three equations produce the same parabola.
Similar Questions
The vertex of the parabola below is at the point (1, 3), and the point (2, 6) is on the parabola. What is the equation of the parabola?A.y = 3(x - 1)2 + 3B.y = 6(x - 1)2 + 3C.y = 3(x + 1)2 - 3D.x = 2(y - 3)2 + 1SUBMITarrow_backPREVIOUS
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left parenthesis, x, comma, y, right parenthesis(x,y) point.y, equals, 2, x, squared, minus, 6y=2x 2 −6
Which of the following is the equation of a parabola?Question 5Select one:a.x = a(y + b)2 + cb.x = a(y + b)2- cc.x = a(y − b)2 - cd.x = a(y − b)2 + c
If the parabola is given by x2-5x+6, find the factors.
Graph parabola by completing the square. Label the vertex, the axis of symmetry, and two other points for the equation y = x2 + 6x + 4.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.