One form of the equation of a parabola is
y = ax² + bx + c
The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)
Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)
Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1
The equation is
y = -x² + 5x - 6
Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6
y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.
Answer: y = -(x - 2.5)² + 0.25
Answer:
44
Step-by-step explanation:
6x +22 + 7x + 16 = 90
13x +38 =90
13x = 52
x = 4
7 x 4 +16 = 44
Answer:
3x+4x+7
Step-by-step explanation:
First, a Trinomial consists of three terms.
so we have <u>blank</u>+<u>blank</u>+<u>blank</u>
Next we need to add the coefficients.
<u>3</u>+<u>4</u>+<u>blank</u>
Add the variables.
3x+4x+<u>blank</u>
And lastly, add the constant.
3x+4x+7
Good luck!
Answer:
0.15-0.75p? YES
-0.45-0.6+0.75P? NO
-3(-0.05+0.25p)? YES
-3(0.15)+(-3)(0.2)+(-3)(0.25p)? NO
Step-by-step explanation:
-3(0.15-0.2+0.25p)
=-0.45+0.6-0.75p
=0.15-0.75p
1. 0.15-0.75p=0.15-0.75p? YES
2. -0.45-0.6+0.75P=0.15-0.75p?
-1.05+0.75p=0.15-0.75p? NO
3. -3(-0.05+0.25p)=0.15-0.75p?
0.15-0.75=0.15-0.75p? YES
4. -3(0.15)+(-3)(0.2)+(-3)(0.25p)=0.15-0.75p?
-0.45-0.6-0.75p=0.15-0.75p?
-1.05-0.75p=0.15-0.75p? NO