To find the x-intercept(s), set y = 0 and solve for x:
0 = -x^2 + 6x + 7
Factor the equation:
0 = -(x - 1)(x - 7)
Setting each factor to zero:
x - 1 = 0 gives x = 1
x - 7 = 0 gives x = 7
So the x-intercepts are x = 1 and x = 7.
To find the vertex of the parabola, we first need to find the x-coordinate of the vertex. The x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b / (2a). In this case, a = -1 and b = 6, so:
x = -6 / (2*-1) = 3
Now substitute x = 3 back into the equation to find the y-coordinate of the vertex:
y = -3^2 + 6*3 + 7
y = -9 + 18 + 7
y = 16
Therefore, the vertex of the parabola is at (3, 16).
find the x-intercept(s) and the vertex of the parabola
y = -x^2 + 6x + 7
x-intercept(s) =
vertex =
1 answer
1 answer