Need help with the below 5 questions. Please include the work and the answer is typed out! Thanks:

1:

Consider a large parabolic reflector in the shape of a headlight used by a construction crew late at night. The lamp is designed in such a way that its light source is placed at the focus of the parabola, which lies 3-1/4 inches from its vertex. Suppose the lamp is to be 16-1/8 inches deep. How wide will the reflector be? a. approximately 16.125 inches b. O approximately 19.4 inches C. O approximately 14.5 inches d. O approximately 29 inchesDetermine the vertex, axis and the direction in which the given parabola opens. szy+3=0 a. O vertex: (0, 3); axis: y : 3; opens to b. O vertex: (0, 3); axis: x : 0; opens the right upward c. O vertex: (0, 3); axis: y = 3; opens to d. O vertex: (0, 3); axis: x = 0; opens the right upward Determine the vertex, axis, and the direction in which the given parabola opens. y1+2x-4y+6=0 I vertex: (1, 2); axis: y : 2; opens to I vertex: (1, 2); axis: x : 1; opens the left downward vertex: (1, 2); axis: y : 2; opens to vertex: (1, 2); axis: x : 1; opens the left downward \fWrite the given equation in standard form. Determine the direction in which the parabola opens. x1+2x3y+19=0 a. O upward b. O to the right 1:. O downward d. O to the left