<span>We have
</span>
Let's take 6 out from the series
<span>Now multiply and divide by 9
</span>
<span>all 1s add up to n
</span>
Complete the square to rewrite the quadratic:
2 <em>x</em>² + 3 <em>x</em> + 5 = 2 (<em>x</em>² + 3/2 <em>x</em>) + 5
... = 2 (<em>x</em>² + 3/2 <em>x</em> + 9/16 - 9/16) + 5
... = 2 (<em>x</em>² + 3/2 <em>x</em> + (3/4)²) + 5 - 9/8
... = 2 (<em>x</em> + 3/4)² + 31/8
Any real number squared becomes non-negative, so the quadratic expression has a minimum value of 31/8, which is greater than 0, and so there are no (real) <em>x</em> for which <em>y</em> = 0.
C, because everything inside the parenthesis is multiplied by -3.
Answer:
Step-by-step explanation:
We can use the quadratic formula or factor, This looks hard to factor so we should use the quadratic formula.
ax^2 + bx + c
so
a=4
b=-9
c=2
you can try it by hand or use this:
https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php
you get x=2 and x=0.25 these are the x intercepts (where Y is zero and where the graph crosses the x axis)
so mark x=2 and x=0.25 with a dot on a number line and you can draw a straight line between them since that is the part of the graph that is below the x axis (because the equation has <0) it is a positive parabola because the "a" value is positive and the presence of a "b" value means part of the graph will be below the x axis
