I'm trying this again, I'd like the quadratic form, so i can then work the intercepts myself. SO:
what's the quadratic form of
1/4(x+3)^2-4
I need it to find the intercepts of the parabola it describes.
Check: I think the parabola is 1/4 scaled, moved 3 to the left and down 4 compared to a y=x^2 parabola. Is this ok?
Thanks for helping before.
If the 4(x+3)^2 is in the denominator, it isn't a parabola. I presume you mean
(1/4)(x+3)^2 -4
In that case, your answer is correct. The parabola is vertically "squashed" by a factor of 1/4, and has its vertex at x=-3 and y = -4
drwls
Thank you very much- you're right, it was a typo!
Can you sterr me to making a quadratic expression from it, so's I can get the intercepts?
Thanks
To find the intercepts of the given quadratic function, you need to set y (or f(x)) equal to zero and solve for x. The x-values at which the function intersects the x-axis are the x-intercepts or zeros of the function.
So, let's solve for x:
(1/4)(x+3)^2 - 4 = 0
First, we can multiply both sides of the equation by 4 to eliminate the fraction:
(x+3)^2 - 16 = 0
Next, let's expand the square:
x^2 + 6x + 9 - 16 = 0
Simplifying further:
x^2 + 6x - 7 = 0
Now, the equation is in quadratic form and we can find the intercepts. To solve this quadratic equation, you have a couple of options: factoring, completing the square, or using the quadratic formula.
Since this equation does not easily factor, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = 6, and c = -7. Substituting these values into the formula, we get:
x = (-6 ± √(6^2 - 4*1*(-7))) / (2*1)
x = (-6 ± √(36 + 28)) / 2
x = (-6 ± √(64)) / 2
x = (-6 ± 8) / 2
Simplifying further:
x = (-6 + 8) / 2 or x = (-6 - 8) / 2
x = 1 or x = -7
Therefore, the intercepts of the parabola described by the quadratic function (1/4)(x+3)^2 - 4 are x = 1 and x = -7.