Given the qaudratic function f(x)=x^2-6x+9 find a value of x such that f(x)=25
You mus find values where is:
x^2-6x+9=25
x^2-6x+9-25=0
x^2-6x-16=0
In google type:
"quadratic equation online"
When you see list of results click on:
webgraphingcom/quadraticequation_quadraticformula.jsp
In rectacangle type: x^2-6x-16=0
an click option solve it
Solutions is x= -2 and x=8
y=x^2-6x+9
for x= -2
y=[(-2)^2]-6*(-2)+9
y=4+12+9=25
for x=8
y=8^2-6*8+9
y=64-48+9=25
I write: y=x^2-6x+9
but you can write:
f(x)=x^2-6x+9
To find a value of x such that f(x) = 25 in the quadratic function f(x) = x^2 - 6x + 9, we can set the equation equal to 25 and solve for x.
So, we have:
x^2 - 6x + 9 = 25
Now, we want to rearrange the equation to get it in standard quadratic form, which is ax^2 + bx + c = 0.
By subtracting 25 from both sides of the equation, we get:
x^2 - 6x + 9 - 25 = 0
Simplifying further, we have:
x^2 - 6x - 16 = 0
Now the equation is in standard quadratic form.
To solve this equation, we can either factorize it or use the quadratic formula. Let's use the quadratic formula, since factoring might not be immediately obvious here.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = -6, and c = -16. Substituting these values into the quadratic formula, we have:
x = (-(-6) ± √((-6)^2 - 4(1)(-16))) / (2(1))
Simplifying the equation further:
x = (6 ± √(36 + 64)) / 2
x = (6 ± √(100)) / 2
x = (6 ± 10) / 2
This gives us two possible solutions:
x₁ = (6 + 10) / 2 = 16 / 2 = 8
x₂ = (6 - 10) / 2 = -4 / 2 = -2
Therefore, in the quadratic function f(x) = x^2 - 6x + 9, the values of x that satisfy f(x) = 25 are x = 8 and x = -2.