8
1 point
Question at position 8
The graph of a quadratic function is shown on the grid.
graph of a parabola through (-5,0), (-3,-8) and (-1,0)
What is the minimum value of this quadratic?
To find the minimum value of the quadratic function, we need to find the vertex of the parabola.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function in the form ax^2 + bx + c.
In this case, we can see that the parabola passes through the points (-5,0), (-3,-8), and (-1,0), so our three points are (-5,0), (-3,-8), and (-1,0). We can use these points to set up a system of equations to find the quadratic function.
Plugging in the values for these points, we get the following equations:
0 = a(-5)^2 + b(-5) + c
-8 = a(-3)^2 + b(-3) + c
0 = a(-1)^2 + b(-1) + c
Solving this system of equations, we get a = 2, b = -8, and c = 10.
Therefore, the quadratic function is f(x) = 2x^2 - 8x + 10.
Now we can use the formula x = -b/2a to find the x-coordinate of the vertex:
x = -(-8) / 2(2) = 8 / 4 = 2
Plugging in x = 2 into the quadratic function, we get:
f(2) = 2(2)^2 - 8(2) + 10 = 8 - 16 + 10 = 2
Therefore, the minimum value of the quadratic function is 2.