State the vertex, direction of opening, axis of symmetry, y intercept, and maximum or minimum value for each of the following:

Question

anonymous · Answer

$$y=(x+4)^{2}+1$$

campbell_st · Answer

expand the right hand side

$$y = x^2 +8x + 17$$

the coefficient of x^2 determines concavity.... +ve concave up -ve concave down

the parabola is concave up

x = -b/2a gives the line of symmetry of the parabola.... (-b/2a comes from the general quadratic formula)

so x = -8/(2 x 1)   the line of symmetry is x = -4

as the parabola is concave up it will have a minimum... 

The vertex is on the line x = -4  so substitute into the equation to find the coordinates of the vertex... (-4, 1) 

the y value from the above is the minimum value... 

to find the y- intercept, let x = 0 and solve.... intercept y = 17