Explain in detail how to find the vertex: y=-2x^2 + 2x + 3

1 answer:

7 0

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{+3} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)$

$\bf \left(-\cfrac{2}{2(-2)}~~,~~3-\cfrac{2^2}{4(-2)} \right)\implies \left( \cfrac{1}{2}~~,~~3+\cfrac{4}{8} \right)\implies \left(\cfrac{1}{2}~~,~~\cfrac{28}{8} \right) \\\\\\ \left(\cfrac{1}{2}~~,~~\cfrac{7}{2} \right)\implies \left(\frac{1}{2}~,~3\frac{1}{2} \right)$

You might be interested in

Factor 6p^2 +15p+9????

Ivanshal [37]

To factor the trinomial, you can use the ac method where you multiply the first and last terms together (6 and 9) and add up to 15.
In this case ac= 54
2 numbers that multiply to 54 and add up to 15 would be 6 and 9 so place these numbers where the 15 would be:
$6p^{2} +9p + 6p+9$
Then group terms to simplify:
$(6p^{2} +9p)(6p+9)
$
Simplify any like terms:
$3p(2p+3) 3(2p+3)$
And group together again:
$(3p+3)(2p+3)$
You can simplify a 3 out of the first expression one more time to get:
$3(p+1)(2p+3)$
Which would be the factored form. I hope this helps :)

8 0

3 years ago

Read 2 more answers

Cassie received a 20%-off coupon and a $10-off coupon from a department store. She visits the department store during a tax-free

UNO [17]

Answer:

B. The original purchase total must be at most to $44 before the discounts are applied.

Step-by-step explanation:

Solve the inequality by adding $10, then dividing by 0.8.

0.8x -$10 ≤ $25.20

0.8x ≤ $35.20 . . . . . . . . add $10

x ≤ $35.20/0.8 . . . . . . . divide by 0.8

x ≤ $44 . . . . . . . . . the before-discount purchase must be at most $44

4 0

3 years ago

Barbara Bailey joined a bowling league. She paid a $18.00 entry fee plus $7.50 a week for 16 weeks. She purchased a bowling ball

larisa [96]

If you add them all up it comes out to $339.94

7 0

3 years ago

Read 2 more answers

A ladder leaning against a wall forms a triangle and exterior angles with the wall and the ground. What are the measures of the

Paha777 [63]

11x° is interior angle of ladder to the ground
and 7X° is interior angle of ladder to the wall

exterior angle of a ladder to wall is 180-7x
and exterior angle of a ladder to ground is 180-11x

7 0

3 years ago

What is the slope of x+y=7,x-y=8

slava [35]

Step-by-step explanation:

The slop is M= 1÷x-y-xy

5 0

3 years ago