How?? I only know how to convert standard form functions into intercept form, but I do not understand how to do this.
Convert the functions into standard form.
1.y=2(x-4)(x+3)
2.y-2=-3(x+4)^2
Both of your equations are quadratics
the standard form, sometimes called the vertex form, of a quadratic takes the form
y = a(x-h)^2 + k , where the vertex is (h,k)
your first equation is in intercept form, so the x of the vertex must be midway between -3 and 4 which would be 1/2
sub in 1/2 for x to get y
y = 2(1/2-4)(1/2+3) = -49/2
so y = 2(x - 1/2)^2 - 49/2
another way would be to first expand it
y = 2(x^2 - x - 12) = 2x^2 - 2x - 24
now completing the square ....
y = 2(x^2 - x + 1/4 -1/4) - 24
= 2( x - 1/2_)^2 - 1/2 - 24
= 2(x-1/2)^2 - 49/2 , same as above
for your second, we are almost there, just add 2 to both sides
y = -3(x+4)^2 + 2
Oh okay thank you, it's very clear now!
To convert a function from intercept form to standard form, you need to expand and simplify the equation.
Let's take a look at the examples you provided to help you understand the process.
1. y = 2(x - 4)(x + 3)
In intercept form, the equation is already factored, so you need to expand it using the distributive property.
Start by multiplying the expressions within the parentheses:
y = 2(x^2 - x + 12)
Next, distribute the 2 to each term inside the parentheses:
y = 2x^2 - 2x + 24
Now, the equation is in standard form (ax^2 + bx + c), where "a" is the coefficient of x^2, "b" is the coefficient of x, and "c" is the constant term. In this case, the function in standard form is:
y = 2x^2 - 2x + 24
2. y - 2 = -3(x + 4)^2
In this case, we have a similar process. Start by expanding the equation using the distributive property.
First, square the term inside the parentheses:
y - 2 = -3(x^2 + 8x + 16)
Next, distribute the -3 to each term within the parentheses:
y - 2 = -3x^2 - 24x - 48
Now, move the constant term to the other side of the equation to obtain standard form:
y + 3x^2 + 24x = -46
The equation is now in standard form: y + 3x^2 + 24x = -46.
Remember, converting from intercept form to standard form involves expanding and simplifying the equation.