The equation f(x) = 4x2 − 16x + 9 represents a parabola. What is the vertex of the parabola?
(2, −7)
( −2, 57)
(4, 9)
( −4, −137)
for y = ax^2 + bx + c
the x of the vertex is -b/(2a)
so for yours, the x of the
vertex = 16/8 = 2
I see (2, -7) as the only point where x = 2
I would now sub x = 2 into the equation to make sure I get -7
To find the vertex of a parabola represented by the equation f(x) = 4x^2 - 16x + 9, you can use the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
In our equation, a = 4 and b = -16. We can substitute these values into the formula to find the x-coordinate of the vertex:
x = -(-16) / (2 * 4)
x = 16 / 8
x = 2
Next, substitute the value of x back into the original equation to find the y-coordinate:
f(2) = 4(2)^2 - 16(2) + 9
f(2) = 4(4) - 32 + 9
f(2) = 16 - 32 + 9
f(2) = -7
Therefore, the vertex of the parabola represented by the equation f(x) = 4x^2 - 16x + 9 is (2, -7).