Where is the vertex of the graph of y equals negative x squared plus 2 x plus 5 located?
(1,5) < it's not this one
(1,6)
(-1,3) <--
(-1,2)
Which values best approximate the solutions of -4x^2+7x+5=0?
0.9 and 2.3
0.9 and 5
-0.5 and 2.3 <--
-0.5 and 5
What is the solution set of 5x2 - 20 = 15x?
{1,-4}
{-2,2}
{-1,4} <--
{-2}
y = -x^2 + 2x + 5
the x of the vertex is -b/(2a) = -2/(-2) = 1
plug in x = -1, y = -1+2+5 = 6
vertex is (1,6)
-4x^2+7x+5=0
4x^2 - 7x - 5 = 0
x = (7 ± √129)/8 = appr (7±11)/8
= appr 18/8 or -4/8 or appr 2.5 or -1/2
your choice is good
5x^2 - 20 = 15x
x^2 - 3x - 4 = 0
(x-4)(x+1) = 0
x = 4 or x = -1
ok
Thank you! :D
To find the vertex of a graph of a quadratic equation in the form y = ax^2 + bx + c, you can use the formula x = -b/2a.
In the equation y = -x^2 + 2x + 5, the coefficient of x^2 is -1, the coefficient of x is 2, and the constant term is 5. Plugging these values into the formula x = -b/2a, we get x = -(2)/2(-1), simplifying to x = -2/-2, which equals 1.
To find the y-coordinate, substitute this x-value into the equation y = -x^2 + 2x + 5. So when x = 1, y = -(1)^2 + 2(1) + 5, simplifying to y = -1 + 2 + 5, which equals 6.
Therefore, the vertex of the graph of y = -x^2 + 2x + 5 is (1, 6).
For the quadratic equation -4x^2 + 7x + 5 = 0, to approximate its solutions, you can use factoring, completing the square, or the quadratic formula.
Alternatively, you can use a graphing calculator or software to find the x-intercepts of the graph of the equation. The x-intercepts are the values of x where the graph crosses the x-axis.
From the given answer choices, -0.5 and 2.3 are the best approximate solutions for the equation -4x^2 + 7x + 5 = 0.
To solve the equation 5x^2 - 20 = 15x, you want to bring all terms to one side to form a quadratic equation equal to zero. In this case, subtract 15x from both sides, resulting in 5x^2 - 15x - 20 = 0.
To solve the quadratic equation, you can use factoring, completing the square, or the quadratic formula.
Factoring the quadratic equation 5x^2 - 15x - 20 = 0, we get (x - 4)(5x + 5) = 0. Setting each factor equal to zero gives two equations: x - 4 = 0 and 5x + 5 = 0.
Solving x - 4 = 0 gives x = 4, and solving 5x + 5 = 0 gives x = -1.
Therefore, the solution set of the equation 5x^2 - 20 = 15x is {-1, 4}.