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Harman [31]
2 years ago
11

Write the quadratic function in vertex form. Then identify the vertex.

Mathematics
1 answer:
ddd [48]2 years ago
7 0

Answer:

Step-by-step explanation:

To put the equation into vertex form, we need to complete the square

g(x) = (x^2 - 4x + ...) - 1\\g(x) = (x^2-4x+(\frac{4}{2})^2 ) - 1 - (\frac{4}{2})^2 \\g(x) = (x-2)^2 - 5\\

This is in the form

y = a(x-h)^2 + k\\(h, k)

So, the vertex is (2, -5)

and g(x) = (x-2)^2-5

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Is the point (1,5) a solution to the equation below?
allochka39001 [22]

Answer:

A. No

Step-by-step explanation:

y = 2x + 4

(5) = 2(1) + 4

5 = 2 + 4

5 = 6 (false statement)

7 0
2 years ago
Marina is currently 14 years older than her cousin joey. in 5 years she will be 3 times as old as joey. if you let x represent j
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How many times does the graph of the function below interect or touch the x-axis? y=-2x^2+3x+5
Andrei [34K]

Answer:

Two times at (-1,0) and (2.5,0)

Step-by-step explanation:

When the graph intersects or touches x-axis, y is equal to 0

so y = -2x^2 + 3x + 5

=> 0 = -2x^2 + 3x + 5

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

so a = -2

    b = 3

    c = 5

substitute in the formula

x = [-3 +/- √(3^2 - 4x-2x5)]/2(-2)

x = [-3 +/- √(9 + 40)]/(-4)

x = [-3 +/- 7]/(-4)

x1 = (-3 + 7)/(-4) = 4/-4 = -1

x2 = (-3 - 7)/(-4) = -10/-4 = 5/2 = 2.5

so the graph has two x-intercepts (-1,0) and (2.5,0), therefore it intersects x-axis two times

7 0
2 years ago
A marble is selected at random from a jar containing 4 red marbles, 2 yellow marbles, and 3 green marbles.
s344n2d4d5 [400]

Answer:

4 / 9  probability of getting a red

Step-by-step explanation:

How many marbles are there total?

4 red + 2 yellow + 3 green = 9 marbles total

P( red marble) = 4 red / 9 total = 4/9

7 0
3 years ago
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<span>you'll find the denominator is zero which isn't possible, so you'll get undefined. </span>
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