For the equation Fx x2 8x 7 does the parabola open up or

For the equation: F(x) = x^2 + 8x + 7 does the parabola open up or down? what is the vertex? what is the x intercept?

f(x) = x^2 + 8x + 7

a) since the leading coefficnet of function is positive hence the parabola opens upwards

b) to find y intercept plug x = 0

f(x) = 0^2 +8(0) + 7 = 7

y intercept = (0,7)

c) x coordinate of vertex is given by -b/2a = -8/2 = -4

y coordinate of vertex = -4^2 +8(-4)+7 = 16 - 32 + 7 = -9

therefore, vertex = ( - 4 , - 9 )

d) to find x intercept set f(x) = 0 and solve for x

x^2 + 8x + 7 = 0

x^2 + 7x + x + 7 = 0

(x+7)(x+1) = 0

x = -7 , -1

x intercepts are ( -7,0) and (-1,0)