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

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}.

y 3x 9

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?

The term 3×2 can be thought of as 3x⋅x and the term 6x can be thought of as 3x⋅2 . The 3x is therefore a common factor that can be factored out (reversing the distributive property), and keeping the minus sign in place: 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 b2 – 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

Leave a Comment