Write an equation for the quadratic graphed below
x-intercepts: (-2,0) and (1,0). y-intercept: (0,-2)
tf type of response is this @oobleck
Write an equation for the quadratic graphed below
x-intercepts: (-2,0) and (1,0). y-intercept: (0,1)
Sure! Let's call the quadratic equation y = ax^2 + bx + c, where a, b, and c are constants.
We have the x-intercepts (-2,0) and (1,0), which means that when x = -2 and x = 1, y is equal to 0. We can use this information to set up the following equations:
0 = a(-2)^2 + b(-2) + c
0 = a(1)^2 + b(1) + c
Simplifying these equations, we get:
4a - 2b + c = 0
a + b + c = 0
We also know the y-intercept is (0,-2), which means that when x = 0, y is equal to -2. Using this information, we can set up another equation:
-2 = a(0)^2 + b(0) + c
Simplifying this equation, we get:
c = -2
So, combining all the information, the equation for the quadratic graphed is:
y = ax^2 + bx - 2
To write the equation for the quadratic graphed below, we need to use the information given about the x-intercepts and y-intercept.
The x-intercepts of the graph are given as (-2,0) and (1,0), which means that the graph crosses the x-axis at these points. From this information, we can determine that the factors of the quadratic equation are (x+2) and (x-1) since they are the expressions that would set the equation equal to zero at these x-intercepts.
The y-intercept of the graph is given as (0,-2), which means that the graph crosses the y-axis at this point. The y-intercept provides us with the value of the constant term of the quadratic equation when x is equal to zero, so we can determine that the equation is of the form y = a(x+2)(x-1) - 2, where "a" is a constant.
To find the value of "a" and complete the equation, we can substitute the coordinates of one of the given x-intercepts, for example, (-2,0), into the equation and solve for "a". Plugging in the values, we have:
0 = a(-2+2)(-2-1) - 2
0 = -3a - 2
Solving for "a", we get:
-3a = 2
a = -2/3
Now we can substitute this value of "a" back into the equation to get the final equation:
y = (-2/3)(x+2)(x-1) - 2
Therefore, the equation for the quadratic graphed below is y = (-2/3)(x+2)(x-1) - 2.
the x-intercepts tell us that
y = a(x+2)(x-1)
Now plug in (0,-2) to find a.
-2 = a(2)(-1)
a = 1
so y = (x+2)(x-1)