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Firdavs [7]
3 years ago
13

Determine the quadratic function f whose graph is given. The vertex is (1,-3) and y-intercept is -2

Mathematics
1 answer:
Nesterboy [21]3 years ago
5 0

Answer:

Vertex form: f(x)=(x-1)^2-3

Standard form: f(x)=x^2-2x-2

Step-by-step explanation:

A quadratic function in vertex form is f(x)=a(x-h)^2+k where (h,k) is the vertex.

We are given h=1,k=-3.

Let's plug that in:

f(x)=a(x-1)^2-3.

Now let's find a.

We will use the y-intercept (0,-2) to find a.

f(0)=a(0-1)^2-3

-2=a(0-1)^2-3

-2=a(-1)^2-3

-2=a(1)-3

-2=a-3

1=a

So the function in vertex form is:

f(x)=(x-1)^2-3.

In standard form, we will have to multiply and combine any like terms.

Let's do that:

f(x)=(x-1)(x-1)-3

f(x)=x^2-x-x+1-3

f(x)=x^2-2x-2

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Answer:

Step-by-step explanation:

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a) 90% conf level when n =28

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6 0
3 years ago
How would I graph this?
elena55 [62]

y\leq 2x-5

↝ x-intercept

2x-5=0\\2x=5\\x=\frac{5}{2}

↝ y-intercept

y = -5

↝ y\leq 2x-5 means that the shade/area is below the graph as shown in the first picture.

y\leq -\frac{1}{2}x-3

↝ x-intercept

-\frac{1}{2}x-3=0\\-x-6=0\\-x=6\\x=-6

↝ y-intercept

y = -3

↝ Since it's "≤" therefore. The shade/area is below the graph. For second picture.

First picture is first inequality

Second picture is second inequality.

3 0
3 years ago
In 5 years' time, Kate's father will be 3 times as old as Kate. Four years ago, her father
Brut [27]

Answer: Kate = 40/3  Her father = 50

Step-by-step explanation:

Let Kate's age in the present be K

And Kate's father's age in the present be F

3(K+5) = F+5

6(K-6) = F-6

Rearrange the first equation to get

3K+15 = F+5

3K+10 = F

Substitute that into the second question

6K-36 = 3K+10-6

3K = 40

K = 40/3

So F = 3*40/3+10 = 50

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The Marrieds are planning to serve 380 guests at a breakfast event. They plan to serve tomato juice, which comes in 46 oz. cans.
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7 0
3 years ago
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