A parabola with apex at point C (0; 7) passes through point (-4; -1). At what points will this parabola intersect the x-axis

We use the formulas for the vertex of the parabola.

X0 = -b / 2 * a;

0 = -b / 2 * a, hence the coefficient b = 0.

Y0 = (4 * a * c – b ^ 2) / 4 * a = 4 * a * c / 4 * a = c;

C = 7.

Then the parabola equation has the form:

Y = a * X ^ 2 + 7.

Substitute the value of the point (-4; -1) and determine the coefficient “a”.

-1 = a * 16 + 7;

16 * a = -8;

a = -0.5.

Then Y = -0.5 * X ^ 2 + 7.

Let us equate the equation to zero and determine the points of intersection with the OX axis.

-0.5 * X ^ 2 + 7 = 0;

0.5 * X ^ 2 = 7;

X ^ 2 = 14;

X = ± √14.

Answer: The parabola crosses the OX axis at the points X = √14, X = -√14.