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consider the following function in vertex form. convert it to standard form by multiplying it out, and then identify the vertical intercept.
g(x)=(x - 2)^2-5
you can tell from the vertex form that the vertical intercept is -5
standard form is g(x)=x^2 - 4x - 1 and the vertical intercept is -1.
none of the statements here is correct.
standard form is g(x)=x^2 - 9 and the vertical intercept is -9.
question 2
1 pts
consider the following function in standard form. convert it to factored form by factoring, and identify the zeros.
h(x)=x^2+3x - 10
factored form is h(x)=(x - 2)(x + 5) and the zeros are 2 and -5.
factored form is h(x)=(x - 2)(x + 5) and the zeros are -2 and 5.
none of the statements here is correct.
factored form is h(x)=(x + 2)(x - 5) and the zeros are -2 and 5.

Explanation:

Question 1:

Step1: Expand the vertex - form

We know that $(a - b)^2=a^{2}-2ab + b^{2}$. For $g(x)=(x - 2)^{2}-5$, expand $(x - 2)^{2}$: $(x - 2)^{2}=x^{2}-4x + 4$. Then $g(x)=x^{2}-4x + 4-5=x^{2}-4x - 1$.

Step2: Find the vertical intercept

The vertical intercept is found by setting $x = 0$. Substitute $x = 0$ into $g(x)$: $g(0)=0^{2}-4\times0 - 1=-1$.

Question 2:

Step1: Factor the quadratic function

For the quadratic function $h(x)=x^{2}+3x - 10$, we need to find two numbers that multiply to -10 and add up to 3. The numbers are 5 and -2. So $h(x)=(x - 2)(x + 5)$.

Step2: Find the zeros

Set $h(x)=0$. Then $(x - 2)(x + 5)=0$. Using the zero - product property, if $ab = 0$, then $a = 0$ or $b = 0$. So $x-2 = 0$ gives $x = 2$ and $x + 5=0$ gives $x=-5$.

Answer:

Question 1:

Standard form is $g(x)=x^{2}-4x - 1$ and the vertical intercept is -1.

Question 2:

Factored form is $h(x)=(x - 2)(x + 5)$ and the zeros are 2 and -5.