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7nadin3 [17]
2 years ago
7

A line passes through the points ( p , a ) and ( p , − a ) where p and a are real numbers. If p = 0 , what is the y-intercept? E

xplain your reasoning.
Mathematics
1 answer:
Lapatulllka [165]2 years ago
6 0

The y-intercept of the linear function is y = 0.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

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Which function in vertex form is equivalent to f(x) = x2 + x +1? f(x) = (x + one-quarter) squared + three-quarters f(x) = (x + o
a_sh-v [17]

The function in vertex form is f(x)=(x+\frac{1}{2})^{2}+\frac{3}{4} ⇒ 3rd answer

Step-by-step explanation:

The vertex form of the quadratic function f(x) = ax² + bx + c is

f(x) = a(x - h)² + k, where

  • a is the coefficient of x²
  • (h , k) are the coordinates of the vertex point
  • h=\frac{-b}{2a} , wher b is the coefficient of x
  • k = f(h), that means value f(x) when x = h

∵ f(x) = x² + x + 1

∴ a = 1 , b = 1

∵ h=\frac{-b}{2a}

- Substitute the values of a and b to find h

∴ h=\frac{-1}{2(1)}

∴ h=\frac{-1}{2}

Substitute the value of x in f(x) by the value of h to find k

∵ f( \frac{-1}{2} ) = (\frac{-1}{2})^{2}+\frac{-1}{2}+1

∴ f( \frac{-1}{2} ) = \frac{1}{4}-\frac{1}{2}+1

∴ f( \frac{-1}{2} ) = \frac{3}{4}

- k is the value of f(x) when x = h

∵ h = \frac{-1}{2}

∴ k = f( \frac{-1}{2} )

∴ k = \frac{3}{4}

Substitute the values of a, h and k in the vertex form

∵ f(x) = a(x - h)² + k

∵ a = 1 , h=\frac{-1}{2} , k=\frac{3}{4}

∴ f(x)=1(x-\frac{-1}{2})^{2}+\frac{3}{4}

∴ f(x)=(x+\frac{1}{2})^{2}+\frac{3}{4}

The function in vertex form is f(x)=(x+\frac{1}{2})^{2}+\frac{3}{4}

Learn more:

You can learn more about the quadratic functions in brainly.com/question/9390381

#LearnwithBrainly

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