Find the vertex of this parabola y=-5x^2-10x-15
2 answers:
Answer:
vertex = (- 1, - 10 )
Step-by-step explanation:
given the equation of a parabola in standard form
y = ax² + bx + c : a ≠ 0
Then the x-coordinate of the vertex is
= -
y = - 5x² - 10x - 15 is in standard form
with a = - 5, b = - 10 and c = - 15, hence
= -
= - 1
substitute x = - 1 into the equation for y
y = - 5(- 1)² - 10(- 1) - 15 = - 5 + 10 - 15 = - 10
vertex = (- 1, - 10 )
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Answer:
Here's one way to do it
Step-by-step explanation:
1. Solve the inequality for y
5x - y > -3
-y > -5x - 3
y < 5x + 3
2. Plot a few points for the "y =" line
I chose
\begin{gathered}\begin{array}{rr}\mathbf{x} & \mathbf{y} \\-2 & -7 \\-1 & -2 \\0 & 3 \\1 & 8 \\2 & 13 \\\end{array}\end{gathered}
x
−2
−1
0
1
2
y
−7
−2
3
8
13
You should get a graph like Fig 1.
3. Draw a straight line through the points
Make it a dashed line because the inequality is "<", to show that points on the line do not satisfy the inequality.
See Fig. 2.
4. Test a point to see if it satisfies the inequality
I like to use the origin,(0,0), for easy calculating.
y < 5x + 3
0 < 0 + 3
0 < 3. TRUE.
The condition is TRUE.
Shade the side of the line that contains the point (the bottom side).
And you're done (See Fig. 3).
