Answer:
The quadratic equation is y = - (x - 5)² + 12
Step-by-step explanation:
The vertex form of the quadratic function is
y = a(x - h)² + k, where
- (h, k) are the coordinates of its vertex point
- a is the coefficient of x²
- If a > 0, then the graph of it is open upward and the vertex point will be a minimum point.
- If a < 0, then the graph of it is open downward and the vertex point will be a maximum point.
In the question
∵ The graph is open downward
∴ a < 0 (a is a negative number)
∵ The vertex point is (5, 12)
∴ h = 5 and k = 12
Substitute them in the form of the equation
∴ y = a(x - 5)² + 12
→ To find a you must have a point on the graph of it to substitute
x and y by its coordinates. because we don't have a point on
the graph we can choose a any negative number.
∵ a is a negative number, let us choose it -1
∴ y = - (x - 5)² + 12
The quadratic equation is y = - (x - 5)² + k
