I had a table of values.
X / Y
-3/ 2.5
-2/ 5
-1/ 6.5
0 / 7
It asks without graphing. Does it open upward or downward.
I got that in the quadratic equation. a= -0.5
And if a is smaller than 0. It opens downward
However. The text book says it opens upward. So I'm confused
What was your quadratic equation ?
Make sure that all your points satisfy it, if even one of them does not work, your equation is wrong.
If they do, and a is negative, then it opens downwards. If your a is positive then it opens up
clearly it opens downward, since for equal increments of x, y is increasing, but more and more slowly. That means that soon it will turn around and start decreasing.
To determine whether a quadratic equation opens upward or downward from a table of values, you can look at the sign of the coefficient 'a' in the equation.
In your case, you mentioned the quadratic equation "a = -0.5." However, it appears there might be a misunderstanding or a mistake in the value of 'a.' Let's clarify it with the correct calculation.
To find the equation of a quadratic function from a given set of points, we can use the general form of a quadratic equation: y = ax^2 + bx + c.
Using the given x and y values from your table, we can substitute them into the equation and form a system of equations:
For (-3, 2.5):
2.5 = a * (-3)^2 + b * (-3) + c
For (-2, 5):
5 = a * (-2)^2 + b * (-2) + c
For (-1, 6.5):
6.5 = a * (-1)^2 + b * (-1) + c
For (0, 7):
7 = a * (0)^2 + b * (0) + c
Simplifying these equations gives you a system of equations to solve simultaneously:
2.5 = 9a - 3b + c
5 = 4a - 2b + c
6.5 = a - b + c
7 = c
With these equations, you can substitute known values into the equation and solve for the coefficients 'a,' 'b,' and 'c.'
By solving this system, you will find the actual values of 'a,' 'b,' and 'c,' which will determine whether the quadratic equation opens upward or downward using the coefficient 'a.'