math 103 - ramiro Moreno , Wednesday, September 26, 2007 at 7:16am
hey man I don't know how to do this problem please I need help
1 pt) Given the function ,
what is its vertex? (____,________)
List its -intercept(s) as a comma separated list. If there are none, type none
___________
List its -intercept(s) as a comma separated list. If there are none, type none .
________________
1 pt) Consider the quadratic equation .
Complete the square to express the quadratic in standard form .
=
=
=
There are no functions listed herein.
To find the vertex of a quadratic function and its x-intercepts, we first need to have the quadratic function in the standard form:
f(x) = ax^2 + bx + c
Once we have the quadratic function in this form, we can use the formulas to find the vertex and x-intercepts.
For finding the vertex:
The x-coordinate of the vertex is given by the formula: x = -b / (2a)
And to find the y-coordinate of the vertex, we substitute the x-coordinate into the quadratic function: y = f(x)
To find the x-intercepts:
We set the quadratic function equal to zero and solve for x to find the x-intercepts. We can use factoring, completing the square, or the quadratic formula to solve for x.
Now let's apply this process to the given problem.
1) Given the function: (no function equation is provided)
Unfortunately, without the actual function equation, we cannot find the vertex or x-intercepts. Please provide the actual function equation.
2) Consider the quadratic equation:
To complete the square and express the quadratic in standard form, we follow these steps:
a) Start with the quadratic equation:
ax^2 + bx + c = 0
b) Divide both sides of the equation by 'a' (if a ≠ 0) to make the coefficient of the x^2 term equal to 1:
x^2 + (b/a)x + c/a = 0
c) To complete the square, we need to add and subtract a value to the equation. The value we add and subtract is (b/2a)^2.
The coefficient of the x term in our equation is (b/a). So, we add and subtract ((b/2a)^2) to the equation:
x^2 + (b/a)x + ((b/2a)^2) - ((b/2a)^2) + c/a = 0
d) Factor the perfect square trinomial:
(x + b/2a)^2 - ((b/2a)^2) + c/a = 0
e) Simplify the equation:
(x + b/2a)^2 - (b^2/4a^2) + c/a = 0
f) Now the equation is in the standard form:
(x + b/2a)^2 = (b^2 - 4ac) / 4a^2
Therefore, the quadratic equation is now in standard form.