Y-Intercept problems, solved and explained

Recent questions in Y-Intercept

enclinesbnnbk 2022-05-15 Answered

This is equation of a curve $\sqrt{y} + \sqrt{x} = \sqrt{A}$
$A$ is a positive constant
$T$ is a tangent of the curve from any point on it
$B$ is the y-intercept of $T$
$C$ is the x-intercept of $T$
Prove that $B + C = A .$ .

Defensorentx9 2022-05-10 Answered

Given $f (x) = \frac{1}{4} (x + 4)^{2} - 2$
Find: vertex, $y$ -intercept, $x$ -intercepts (if any), axis of symmetry
What I have so far:
Vertex: $(- 4, - 2)$
$y$ -intercept: $(0, 2)$
$x$ -intercept: $2$
Axis of symmetry $x = - 4$

Jay Barrett 2022-05-09 Answered

Find the $y$ -intercept of the curve that passes through the point $(2, 1)$ with the slope at $(x, y)$ of $\frac{- 9}{y^{2}}$
$\frac{d y}{d x} = \frac{- 9}{y^{2}}$
$\int y^{2} d y = \int - 9 d x$
$\frac{y^{3}}{3} = - 9 x + C_{1}$
$y^{3} = - 27 x + C$ $(C = 3 C_{1})$
$y = (- 27 x + C)^{1 / 3}$
$1 = (- 27 (2) + C)^{1 / 3}$
$C = 54$
$0 = (- 27 x + 54)^{1 / 3}$
$y - i n t e r c e p t = (- 2, 0)$
Where is mistake?

Marissa Singh 2022-05-09 Answered

The gradient is $m = - 4 / 3$ , and the point given is $(3 / 2, 3)$
Let $c$ be the $y$ -intercept
$y = m x + c$
$y = (- 4 / 3) x + c$
If I substitute $x$ and $y$ from the point given, $3 = (- 4 / 3) (3 / 2) + c$ and look for $c$ , I get $c = 5$
But according to my answer sheet, $c = 33 / 8$ by using $y - y_{1} = m (x - x_{1})$
Why are the two methods giving different answers?

Jamir Melendez 2022-05-09 Answered

An equation to the tangent line of $h (x) = \tan (x) + \cos (x)$ is given by $y = m x + b$ where $m$ is the slope and $b$ is the $y$ -intercept. If $x = \frac{π}{4}$ find $m$ .

Defensorentx9 2022-05-08 Answered

Two questions involving quadratics. Next to a diagram of a parabola with a ma point with the y intercept of $(0, p)$ and roots $(- 1, 0)$ and $(p, 0)$ it says:3a) Show that the equation of the parabola is $y = p + (p - 1) x - x^{2}$
3b) For what value of $p$ will the line $y = x + p$ be a tangent to this curve.

dresu9dnjn 2022-05-07 Answered

Need to find the $y$ -intercept of the tangent to $y = \frac{18}{x^{2} + 2}$ at point $(1, 6)$ .
I keep getting $0$ , but I don't think that's right.

Azzalictpdv 2022-04-06 Answered

Let $f (x) = x^{2} + x - 6$ .
a. Write down the $y$ -intercept of the graph of $f$ .
how do we figure this out? I know $f (x)$ means $y$ , so do we use the quadratic formula? $x^{2} + x - 6$ .
b. Solve $f (x) = 0$ .
We plug $0$ into the $x$ ’s in the original formula, right?

Jaime Coleman 2022-04-06 Answered

how to draw functions on a coordinate plane, and he mentioned something about the Y-Intercept being an important step in creating/solving a function. But, what exactly is a Y-Intercept?