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3 years ago

Find the vertex of the parabola.

Mathematics

1 answer:

Gnesinka [82]3 years ago

4 0

Answer:

The vertex is (3,4)

Step-by-step explanation:

f (x) = x^2 - 6 x + 13

Completing the square

-6/2 = -3 and squaring it = 9

= x^2 -6x +9 +4

= ( x-3) ^2 +4

The equation is now in vertex form

a( x-h) ^2 +k

where the vertex is ( h,k)

The vertex is (3,4)

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2 years ago

The admission fee at a small to the school play is $1.50 for children (x) and $4.00 for adults (y). On opening night, the revenu

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2 years ago

What is the y-intercept of the line perpendicular to the line...

Dominik [7]

Answer:

D) 5

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes.

The line: $y=\frac{3}{4} x+3$ has a slope of $\frac{3}{4}$ as it is in y=mx+b form, where m is the slope, and b is the y-intercept.

Since the slope is $\frac{3}{4}$ , we see that the negative reciprocal slope is $-\frac{4}{3}$ , as $\frac{4}{3}$ is the reciprocal (flip the numerator and denominator).

From here, we can use point slope form: $y - y1 = m(x- x1)$ , where $(y1, x1)$ is the point. In this case, (3, 1) is the point.

Thus, we have: $y-1 =-\frac{4}{3}(x-3)$ as our final equation.

Simplifying: $y-1 = -\frac{4}{3}x+4$

And: $y=-\frac{4}{3}x+5$ , which gives us the y-intercept to be 5.

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2 years ago

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3 years ago

Read 2 more answers

For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).

Ivanshal [37]

Answer:

$\displaystyle F(b + 3) = b^2 + 4b + 7$

Step-by-step explanation:

We are given the function:

$\displaystlye F(x) = x^2 - 2x + 4$

And we want to find F(<em>b</em> + 3).

We can substitute:

$\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4$

Expand:

$\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4$

Rearrange:

$\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)$

Combine like terms. Hence:

$\displaystyle = b^2 +4b + 7$

In conclusion:

$\displaystyle F(b + 3) = b^2 + 4b + 7$

6 0

2 years ago