Write the equation of the parabola graphed below given the y-intercept is (0, 1) Brainliest gets 45 points so please help ASAP

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9.5 Graphing Parabolas

LEARNING OBJECTIVES

Graph a parabola.

Find the intercepts and vertex of a parabola.

Find the vertex of a parabola by completing the square.

The Graph of a Quadratic Equation

We know that any linear equation with two variables can be written in the form

y

=

m

x

+

b

and that its graph is a line. In this section, we will see that any quadratic equation of the form

y

=

a

x

2

+

b

x

+

c

has a curved graph called a parabola.

Two points determine any line. However, since a parabola is curved, we should find more than two points. In this text, we will determine at least five points as a means to produce an acceptable sketch. To begin, we graph our first parabola by plotting points. Given a quadratic equation of the form

y

=

a

x

2

+

b

x

+

c

, x is the independent variable and y is the dependent variable. Choose some values for x and then determine the corresponding y-values. Then plot the points and sketch the graph.

y =  x² - 2x + 1

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

From the graph (h, k) = (2, - 1), thus

y = a(x - 2)² - 1

To find a substitute a point on the curve (0, 1) into the equation

1 = 4a - 1 ( add 1 to both sides )

4a = 2 ( divide both sides by 4 )

a =  = , hence

y = (x - 2)² - 1 ← in vertex form

Expand the factor and simplify

y = (x² - 4x + 4) - 1

 =  x² - 2x + 2 - 1

 =  x² - 2x + 1 ← in standard form

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068