Caun yuo help me , please ? Make a list of everything you know, or can figure out, about this parabola at right. Aim for 10 - 15.

Question

10 - 15.

Make a list of everything you know, or can figure out, about this parabola at right. Aim for 10 - 15.

Answer 1

concave down

its "a" value is negative

narrower than y = x² so |a| > 1

axis of symmetry is x = 5

one x-intercept at (3,0)

the 2nd x-intercept at (7,0) (using symmetry)

factored form: y = a(x-3)(x-7)

vertex at (5,12)

Vertex form: y - 12 = a(x - 5)²

Its y-intercept is < 0

In standard form: y = ax² + bx + c , its c-value is negative

Because it has 2 x-intercepts, (b² - 4ac) > 0

Because the 2 x-intercepts occur at rational values for x (integer values, in fact), (b² - 4ac) is a perfect square

If you graphed the concave up parabola with a vertex at (5,-12) and the same x-intercepts as this one on the same set of axes, the 2 graphs would form a football-ish shaped thing that would be pretty cool.

Answer 2

Vertex form: y = a(x-h)² + k

Vertex (5,12)

Crossing points of (4,9) and (6,9)

x-axis crossing of (3,0) (7,0)

Solve for a: 0 = a(3-5)² + 12 -12 = a(2)² a = -3

y = -3(x-5)² +12

You can figure other things out if this isn't enough