This task gives you the opportunity to:
• Find graphical properties of a quadratic function given by its formula.
y-x-3r-10 is a quadratic function.
Say whether each of these statements about the function is true or false.
If a statement is false, give a true version of the statement.
1. The graph of y=x²-3x-10 cuts the y-axis at (0, -10).
2. y=x²-3x-10 can be written as y=(x-2)(x+5).
3. When x= -3, y=-10.
4. The solutions of the equation x²-3x-10-0 are x=2 and x = 5.
5. The function has a minimum value but no maximum value.
6. The graph of y=x²-3r-10 is below the x-axis for -2 sxs5.

Question

contestada

Respuesta :

facundo3141592 facundo3141592 · Answer 1 · 2022-09-06T20:25:26+02:00

For the quadratic equaton:

1) True.

2) False.

3) True.

4) False.

5) True.

6) True.

Here we have the quadratic equation:

y = x^2 - 3x - 10

1) The y-intercept is what we get when we evaluate zero.

y = 0^2 - 3*0 - 10 = -10

Then yes, it is true that the graph cuts the y-axis at (0, -10).

2) It only can be rewritten in that way if x = 2 and x = -5 are zeros of the parabola:

for x = 2.

y = 2^2 - 3*2 - 10 = 4 - 6 - 10 = -12

This is not zero, then this statement is false.

3) Here we need to evaluate in x = -3, we will get:

y = (-3)^2 - 3*(-3) - 10 = 9 - 9 - 10 = -10

So this is true.

4) This is equivalent to statement 2, we already know that x = 2 is not a zero of the quadratic equation, then this is false.

5) This is true, the quadratic equation has a positive leading coefficient, which means that the parabola opens upwards.

6) Let's see the value when x = 5

y = 5^2 - 3*5 - 10 = 0

And when x = -2

y = (-2)^2 - 3*(-2) - 10 = 0

So these are the two zeros, which means that between these two values the function is negative. So this is true.

If you want to learn more about quadratic functions:

https://brainly.com/question/1214333

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