# How to Solve Parabolic Equations

• yeuVi
In summary, the conversation is discussing a problem involving equations for x and y, with a given hint. The second equation is a fraction with a restriction on the values of t1 and t2. The final answer is given as t1 = √6 and t2 = -√6.
yeuVi
Help with paremetic

I need help with these... I can't read them...

$$\color{blue} a): \ \ \ \ \mathsf{ Eq \ for \ "x" \ indicates \ t_{1} = -t_{2} \ \ \ \ \ \ \ Eq \ for \ "y" \ uses \ next \ hint }$$

$$\color{blue} b): \ \ \ \ \frac { t_{1}^{3} \ - \ t_{2}^{3} } { t_{1} \ - \ t_{2} } \ = \ t_{1}^{2} \ + \ t_{1}t_{2} \ + \ t_{2}^{2} \ \ \ \ \ \ \ ( t_{1} \ \ne \ t_{2} )$$

$$\color{blue} c): \ \ \ \ (Answers) \ \longrightarrow \ \ (t_{1} \ = \ \sqrt{6}) \ \ and \ \ (t_{2} \ =\ -\sqrt{6})$$

edited to add "tex" by HallsofIvy

Last edited by a moderator:
wrap $$around each line, because that's just a mess. I wonder if there is something wrong on your computer [tex]\color{blue} a): \ \ \ \ \mathsf{ Eq \ for \ "x" \ indicates \ t_{1} = -t_{2} \ \ \ \ \ \ \ Eq \ for \ "y" \ uses \ next \ hint }$$

$$\color{blue} b): \ \ \ \ \frac { t_{1}^{3} \ - \ t_{2}^{3} } { t_{1} \ - \ t_{2} } \ = \ t_{1}^{2} \ + \ t_{1}t_{2} \ + \ t_{2}^{2} \ \ \ \ \ \ \ ( t_{1} \ \ne \ t_{2} )$$

$$\color{blue} c): \ \ \ \ (Answers) \ \longrightarrow \ \ (t_{1} \ = \ \sqrt{6}) \ \ and \ \ (t_{2} \ =\ -\sqrt{6})$$

## What is a parabolic equation?

A parabolic equation is a quadratic equation that describes the shape of a parabola. It has the form y = ax^2 + bx + c, where a, b, and c are constants.

## How do you solve a parabolic equation?

To solve a parabolic equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Alternatively, you can factor the equation and solve for x.

## What is the vertex of a parabola?

The vertex of a parabola is the point on the graph where the parabola changes direction. It is also the maximum or minimum point of the parabola, depending on the direction of the curve.

## What is the axis of symmetry of a parabola?

The axis of symmetry of a parabola is a vertical line that divides the parabola into two equal halves. It passes through the vertex of the parabola and is perpendicular to the directrix.

## How can I graph a parabolic equation?

To graph a parabolic equation, you can plot points on the coordinate plane by substituting different values of x into the equation and solving for y. You can also use the vertex and axis of symmetry to help you plot the parabola.

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