5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.
We need to determine the equation, in vertex form, for the following parabolas.
How to find the equation, in vertex form?
We can find the parabola's equation in vertex form following two steps:
Step 1: Use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)²+k.
Step 2: Find the value of the coefficient a by substituting the coordinates of the point into the equation written in step 1 and solving for a.
Now, substitute (−2, 5) in y=a(x−h)²+k
⇒y=a(x−(-2))²+5
Now, substitute (2, 0) in y=a(x−(-2))²+5.
0=a(2+2)²+5
⇒a=-5/16
So, y=-5/16(x+2)²+5
⇒16y=-5(x²+4x+4)+5
⇒16y=-5x²-20x-20+5
⇒5x²+20x+16y-15=0.
Therefore, 5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.
To learn more about the vertex form visit:
https://brainly.com/question/13921516.
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