Answer:
y = 4(x - 3)² - 5
Step-by-step explanation:
Given the vertex, (3, -5), and the other point, (4, -1):
Substitute these values into the vertex form of the quadratic equation:
y = a(x - h)² + k
where:
(h, k) = vertex
a = determines the direction of which the graph opens (if a > 1, the graph opens up; a < 1, the graph opens down). The value of a also determines the width of the parabola. If 0 < a < 1, the graph will be wide; if a > 1, the graph will be narrow.
h = indicates a horizontal translation.
k = indicates a vertical translation.
Next, substitute the values of the vertex, (3, -5), and the other given point, (4, -1) into the vertex form and solve for the value of a:
y = a(x - h)² + k
-1 = a(4 - 3)² - 5
-1 = a( 1 )² - 5
-1 + 5 = a1 - 5 + 5
4 = a
Therefore, the equation of the given graph is: y = 4(x - 3)² - 5.
Note:
If the equation needs to be in standard form, ax² + bx + c, simply expand the binomial factors in the vertex form, and combine like terms. Doing so will result in the following standard form: y = 4x² - 24x + 31.
