The problem contains three questions. The first question requires us to identify whether the given quadratic functions are in standard form or factored form. The second question is a true/false question about the definition of x-intercepts. The third question asks us to find the y-intercept of the given quadratic function.

1. Problem Description

The problem contains three questions. The first question requires us to identify whether the given quadratic functions are in standard form or factored form. The second question is a true/false question about the definition of x-intercepts. The third question asks us to find the y-intercept of the given quadratic function.

2. Solution Steps

Question 1:

a. $y = 5x^2 + 4x$ is in standard form. Standard form is $ax^2 + bx + c$. Here, $a=5$, $b=4$, and $c=0$.

b. $y = (x+3)(x-1)$ is in factored form. Factored form is $a(x-r_1)(x-r_2)$ where $r_1$ and $r_2$ are roots. Here, $a=1$, $r_1 = -3$, and $r_2 = 1$.

c. $y = 2(x - \frac{1}{2})(x+3)$ is in factored form. Here, $a=2$, $r_1 = \frac{1}{2}$, and $r_2 = -3$.

d. $y = x^2 + 7$ is in standard form. Here, $a=1$, $b=0$, and $c=7$.

Question 2:

An x-intercept is also called a "root".

This statement is true.

Question 3:

To find the y-intercept of the quadratic function $f(x) = x^2 + 5x - 8$, we need to find the value of $f(x)$ when $x = 0$.

$f(0) = (0)^2 + 5(0) - 8 = 0 + 0 - 8 = -8$

Therefore, the y-intercept is $-8$.

3. Final Answer

Question 1:

a. Standard form

b. Factored form

c. Factored form

d. Standard form

Question 2: True

Question 3: -8