Use the symmetry of each quadratic function to find the maximum or minimum points.
c. y=x^2+4x-21
axis of symmetry ... x = -4 / (2 * 1) = -2
y = (-2)^2 + (4 * -2) - 21 = -25
minimum at ... (-2,-25)
To find the maximum or minimum point of a quadratic function, we can use the symmetry of the graph.
The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.
In this case, our quadratic function is y = x^2 + 4x - 21.
To find the maximum or minimum point, we need to calculate the x-coordinate of the vertex.
The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the formula:
x = -b / (2a)
In our case, a = 1 and b = 4, so we can substitute these values into the formula:
x = -4 / (2 * 1)
x = -4 / 2
x = -2
Now, we have the x-coordinate of the vertex, which is -2.
To find the y-coordinate of the vertex, we substitute the x-coordinate back into the original equation:
y = (-2)^2 + 4(-2) - 21
y = 4 - 8 - 21
y = -25
Therefore, the vertex of the quadratic function y = x^2 + 4x - 21 is (-2, -25).
Since the coefficient of the x^2 term (a) is positive, the parabola opens upwards, meaning the vertex is the minimum point. So, the minimum point is (-2, -25).