Answer:
- 0 real zeros
- 2 complex zeros
Step-by-step explanation:
The "fundamental theorem of algebra" says a polynomial of degree n will have n zeros. If the polynomial has real coefficients, the complex zeros will appear in conjugate pairs.
The graph of this quadratic (degree = 2) does not cross the x-axis, so there are no real values of x that make y=0. That means the two zeros are both complex.
<span>1) 2p = -2.
<span> 4p [ y - k ] = [ x - h) ]² --- > - 4 [ y + 5 ] = [ x + 5 ]²
2) </span></span><span>4p * (y - k) = (x - h)^2 </span>
<span>(h , k) is the vertex </span>
<span>The vertex is halfway between the focus and the directrix (when they're at their closest) </span>
<span>p is that distance </span>
<span>2 - 1 = 1 </span>
<span>4p = 1 </span>
<span>p = 1/4 </span>
<span>(1/4) * (y - k) = (x - h)^2 </span>
<span>y - k = 4 * (x - h)^2 </span>
<span>The vertex is at (6 , 3/2), since that's midway between (6 , 1) and (6 , 2) </span>
<span>y - 3/2 = 4 * (x - 6)^2 </span>
<span>y = (3/2) + 4 * (x - 6)^2
</span><span>
4) </span><span>f(x) = (-1/16)*(x²)
</span><span>
5) </span><span>f(x) = −1/4 x2 − x + 5</span><span>
</span>
The answer to 1/4x - 6 = 3/5 is x = 132/5, or if you want to simplify it to a mixed fraction, it'd be 26 2/5. Here are the steps:
1/4x - 6 = 3/5
+6 +6 Add 6 to each side to isolate the variable x.
1/4x = 6 3/5
(4)1/4x = 6 3/5(4) Multiply by 1/4's reciprocal (4), to isolate the variable x.
x = 33/5 (4)
x = 132/5
x = 26 2/5
