The graph of a certain quadratoc y = ax + bx + c is a parabola with vertex (-4, 0) which passes through the point (1, -75). What is the value of a?
Thanks in advance.
+9466 The general equation of a parabola with a vertex at (-4, 0) is...
y = A(x + 4)2 + 0
We want the parabola to pass through the point (1, -75) , so we want a value of A such that...
-75 = A(1 + 4)2 + 0
-75 = A(5)2
-75 = A(25)
-75/25 = A
-3 = A
So the equation of a parabola with a vertex at (-4, 0) that passes through the point (1, -75) is...
y = -3(x + 4)2 + 0
y = -3(x + 4)(x + 4)
y = -3(x2 + 8x + 16)
y = -3x2 - 24x - 48 Here's a graph to check this: https://www.desmos.com/calculator/ir8koxrnsi
We can see that a = -3 .
+9466 The general equation of a parabola with a vertex at (-4, 0) is...
y = A(x + 4)2 + 0
We want the parabola to pass through the point (1, -75) , so we want a value of A such that...
-75 = A(1 + 4)2 + 0
-75 = A(5)2
-75 = A(25)
-75/25 = A
-3 = A
So the equation of a parabola with a vertex at (-4, 0) that passes through the point (1, -75) is...
y = -3(x + 4)2 + 0
y = -3(x + 4)(x + 4)
y = -3(x2 + 8x + 16)
y = -3x2 - 24x - 48 Here's a graph to check this: https://www.desmos.com/calculator/ir8koxrnsi
We can see that a = -3 .
