Table of Contents

## How many solutions does y 3x 2 6x 3 have?

The quadratic formula gives **two solutions, one when xb1 is addition and one when it is subtraction. This equation is in standard form: ax^{2}+bx+c0. Substitute 3 for a, 6 for b, and -3-y for c in the quadratic formula, frac{-bxb1sqrt{b^{2}-4ac}}{2a}.**

## What is the formula to find the vertex of a quadratic function using H k )?

The standard form of a quadratic function is f(x)=a(x−h)2+k. The vertex (h,k) is located at **h=–b2a,k=f(h)=f(−b2a)**.

## What do you call the graph of a quadratic function?

The graph of a quadratic function is called **a parabola and has a curved shape. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola. I will be showing you how to find the vertex as well as the axis of symmetry that goes through this point.**

## Which graphed which parabola opens downward?

There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and **if the leading coefficient is less than zero, the parabola opens downward.**

## How many solutions does 3x 2 6x 3 have?

This equation has **no solution. A a non-zero constant never equals zero.**

## How many solutions does y 3x 2 have?

These are **three possible solutions to the equation.**

## How do you factor 3x 2 6x?

**3×2−6x=3x**(x−2) .

## What is the solution of Y 3x 1?

Answer: The solutions of y 3x – 1 are **(1, 2) and (0, -1) We will substitute x-coordinate and y-coordinate in the equation y 3x – 1 to check if the given points are the solution of the equation.**

## How do you find the vertex of H and K?

For a given quadratic y ax2 + bx + c, the vertex (h, k) is found by **computing h b/2a, and then evaluating y at h to find k.**

## What is the formula for the vertex of a quadratic equation?

Get the equation in the form **y ax2 + bx + c. Calculate -b / 2a. This is the x-coordinate of the vertex. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.**

## What is the formula of H and K?

The vertex formula to find the vertex coordinates (h,k) (-b/2a, -D/4a) from the standard equation **y ax2 + bx + c, where D b**2 – 4ac.

## What is the H and K of the vertex point?

The vertex of a parabola is the point where the parabola crosses its axis of **symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the U -shape. In this equation, the vertex of the parabola is the point (h,k) . **

## What is another name for a quadratic graph?

The graph of a quadratic function is a curve called **a parabola. Parabolas may open upward or downward and vary in width or steepness, but they all have the same basic U shape.**

## What is a called in a quadratic function?

In algebra, a quadratic equation (from the Latin quadratus for square) is any **equation that can be rearranged in standard form as. where x represents an unknown, and a, b, and c represent known numbers, where a u2260 0. If a 0, then the equation is linear, not quadratic, as there is no. term.**

## What do you call a graph that opens downward?

The graph of a quadratic equation in two variables (y ax2 + bx + c ) is called a **parabola. We say that the first parabola opens upwards (is a U shape) and the second parabola opens downwards (is an upside down U shape).**

## How do you find the downward of a parabola?

The equation with a parabola facing downward will be **(x – h)2 4p(y – k), where 4p is negative.**

## How do you determine if a parabola opens up down left or right?

If **the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.**

## What is the point of the parabola opens downward?

If the parabola opens down, **the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph. The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry.**

## Can quadratic equation have 3 solutions?

The quadratic formula gives **two solutions, one when xb1 is addition and one when it is subtraction. This equation is in standard form: ax^{2}+bx+c0. Substitute 3 for a, 6 for b, and -3-y for c in the quadratic formula, frac{-bxb1sqrt{b^{2}-4ac}}{2a}.**

## How many solutions do quadratics have?

A **quadratic equation can’t have 3 solutions in the real numbers, or even the complex numbers.**

## How many solutions does this equation have?

If solving an equation yields a statement that is true for a single value for the variable, like x 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 3, then the equation has **infinitely many solutions**

## How do you know how many solutions 2 equations have?

A system of two equations can be classified as follows: If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. **If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.**

## How do you factor 3x 2 6x 1?

**Explanation:**

- 3x2u22126xu22129.
- 3(x2u22122xu22123) (taking out the common factor of 3)
- 3(x+1)(xu22123) (looking for factors of 3 to give -2)

## How do you factor 3x 2 6x 9?

**Factoring using the greatest common factor**

- Write each term as the. prime factorization. of the coefficient or constant, listing any variables separately. For example, write. x. y. as. x. y. , and write. x. as. x. x. .
- Identify the factors that all of the terms have in common.
- Multiply those common factors.

## What is the slope for Y =- 3x 1?

3